
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Z
mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZm Z m!Z!m"Z"m#Z#m$Z$m%Z%m&Z&m'Z'm(Z(m)Z)m*Z*m+Z+m,Z,m-Z-m.Z.m/Z/m0Z0m1Z1m2Z2m3Z3m4Z4m5Z5m6Z6m7Z7m8Z8m9Z9m:Z:m;Z;m<Z<m=Z=m>Z>m?Z?m@Z@mAZAmBZBmCZCmDZDmEZEmFZFmGZGmHZHmIZImJZJmKZKmLZLmMZMmNZNmOZOmPZPmQZQmRZRmSZSmTZTmUZUmVZVmWZWmXZXmYZYmZZZm[Z[m\Z\m]Z]m^Z^m_Z_m`Z`maZambZbmcZcmdZdmeZemfZfmgZgmhZhmiZimjZjmkZkmlZlmmZmmnZnmoZompZpmqZqmrZrmsZsmtZtmuZumvZvmwZwmxZxmyZymzZzm{Z{m|Z|m}Z}m~Z~mZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmJZJmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZmZd d lmZd d	 lmZmZd d
 lmZmZmZmZm Z mZmZmZd d lmZmZmZmZmZm	Z	m
Z
mZmZmZmZmZd d lmZmZmZmZmZmZmZd d lmZg  d D] Zee ^ q\ ZZZZZZ Z!Z"Z#Z$Z%Z&Z'Z(Z)Z*Z+Z,Z-Z.Z/Z0Z1Z2Z3Z4Z5Z6Z7Z8Z9g  d d d d d d d d d d d d d d d d d d d d  d! d" d# d$ d% d& d' d( d) d* g D] Zee ^ q\ Z:Z;Z<Z=Z>Z?Z@ZAZBZCZDZEZFZGZHZIZBZCZJZKZLZMZNZOZPZQZRZSZTZUed+  \	 ZZVZWZXZYZZZ[Z\Z]e^Z_e^Z`eaZbn  d,   Zcd- S(.   s   
This code is automatically generated. Never edit it manually.
For details of generating the code see `rubi_parsing_guide.md` in `parsetools`.
i(   t   import_modulet   matchpy(   t   doctest_depends_on(   t   Patternt   ReplacementRulet   CustomConstraintt   is_match(  t   Intt   Sumt   Sett   Witht   Modulet   Scant   MapAndt   FalseQt   ZeroQt	   NegativeQt   NonzeroQt   FreeQt   NFreeQt   Listt   Logt	   PositiveQt   PositiveIntegerQt   NegativeIntegerQt   IntegerQt	   IntegersQt   ComplexNumberQt   PureComplexNumberQt   RealNumericQt   PositiveOrZeroQt   NegativeOrZeroQt   FractionOrNegativeQt   NegQt   Equalt   Unequalt   IntPartt   FracPartt	   RationalQt   ProductQt   SumQt   NonsumQt   Substt   Firstt   Restt   SqrtNumberQt   SqrtNumberSumQt   LinearQt   Sqrtt   ArcCosht   Coefficientt   Denominatort   Hypergeometric2F1t   Nott   Simplifyt   FractionalPartt   IntegerPartt   AppellF1t
   EllipticPit	   EllipticEt	   EllipticFt   ArcTant   ArcCott   ArcCotht   ArcTanht   ArcSint   ArcSinht   ArcCost   ArcCsct   ArcSect   ArcCscht   ArcSecht   Sinht   Tanht   Cosht   Secht   Cscht   Cotht	   LessEqualt   Lesst   Greatert   GreaterEqualt	   FractionQt   IntLinearcQt   Expandt   IndependentQt   PowerQt   IntegerPowerQt   PositiveIntegerPowerQt   FractionalPowerQt   AtomQt   ExpQt   LogQt   Headt   MemberQt   TrigQt   SinQt   CosQt   TanQt   CotQt   SecQt   CscQt   Sint   Cost   Tant   Cott   Sect   Csct   HyperbolicQt   SinhQt   CoshQt   TanhQt   CothQt   SechQt   CschQt   InverseTrigQt   SinCosQt	   SinhCoshQt	   LeafCountt	   Numeratort   NumberQt   NumericQt   Lengtht   ListQt   Imt   Ret   InverseHyperbolicQt   InverseFunctionQt   TrigHyperbolicFreeQt   InverseFunctionFreeQt   RealQt   EqQt   FractionalPowerFreeQt   ComplexFreeQt   PolynomialQt   FactorSquareFreet   PowerOfLinearQt   Exponentt
   QuadraticQt   LinearPairQt   BinomialPartst   TrinomialPartst   PolyQt   EvenQt   OddQt   PerfectSquareQt   NiceSqrtAuxQt	   NiceSqrtQt   Togethert   PosAuxt   PosQt   CoefficientListt
   ReplaceAllt   ExpandLinearProductt   GCDt   ContentFactort   NumericFactort   NonnumericFactorst   MakeAssocListt   GensymSubstt   KernelSubstt   ExpandExpressiont   Apartt
   SmartApartt   MatchQt   PolynomialQuotientRemaindert   FreeFactorst   NonfreeFactorst   RemoveContentAuxt   RemoveContentt	   FreeTermst   NonfreeTermst   ExpandAlgebraicFunctiont   CollectReciprocalst   ExpandCleanupt   AlgebraicFunctionQt   Coefft   LeadTermt   RemainingTermst
   LeadFactort   RemainingFactorst   LeadBaset
   LeadDegreet   Numert   Denomt	   hypergeomt   Expont   MergeMonomialst   PolynomialDividet	   BinomialQt
   TrinomialQt   GeneralizedBinomialQt   GeneralizedTrinomialQt   FactorSquareFreeListt   PerfectPowerTestt   SquareFreeFactorTestt   RationalFunctionQt   RationalFunctionFactorst   NonrationalFunctionFactorst   Reverset   RationalFunctionExponentst   RationalFunctionExpandt   ExpandIntegrandt   SimplerQt   SimplerSqrtQt   SumSimplerQt   BinomialDegreet   TrinomialDegreet   CancelCommonFactorst   SimplerIntegrandQt   GeneralizedBinomialDegreet   GeneralizedBinomialPartst   GeneralizedTrinomialDegreet   GeneralizedTrinomialPartst	   MonomialQt   MonomialSumQt   MinimumMonomialExponentt   MonomialExponentt   LinearMatchQt   PowerOfLinearMatchQt   QuadraticMatchQt   CubicMatchQt   BinomialMatchQt   TrinomialMatchQt   GeneralizedBinomialMatchQt   GeneralizedTrinomialMatchQt   QuotientOfLinearsMatchQt   PolynomialTermQt   PolynomialTermst   NonpolynomialTermst   PseudoBinomialPartst   NormalizePseudoBinomialt   PseudoBinomialPairQt   PseudoBinomialQt   PolynomialGCDt   PolyGCDt   AlgebraicFunctionFactorst   NonalgebraicFunctionFactorst   QuotientOfLinearsPt   QuotientOfLinearsPartst   QuotientOfLinearsQt   Flattent   Sortt   AbsurdNumberQt   AbsurdNumberFactorst   NonabsurdNumberFactorst   SumSimplerAuxQt   Prependt   Dropt   CombineExponentst   FactorIntegert   FactorAbsurdNumbert   SubstForInverseFunctiont   SubstForFractionalPowert*   SubstForFractionalPowerOfQuotientOfLinearst"   FractionalPowerOfQuotientOfLinearst   SubstForFractionalPowerQt   SubstForFractionalPowerAuxQt   FractionalPowerOfSquareQt   FractionalPowerSubexpressionQt   Applyt   FactorNumericGcdt   MergeableFactorQt   MergeFactort   MergeFactorst   TrigSimplifyQt   TrigSimplifyt   TrigSimplifyRecurt   Ordert   FactorOrdert   Smallestt   OrderedQt   MinimumDegreet   PositiveFactorst   Signt   NonpositiveFactorst   PolynomialInAuxQt   PolynomialInQt   ExponentInAuxt
   ExponentInt   PolynomialInSubstAuxt   PolynomialInSubstt   Distribt   DistributeDegreet   FunctionOfPowert   DivideDegreesOfFactorst   MonomialFactort   FullSimplifyt   FunctionOfLinearSubstt   FunctionOfLineart   NormalizeIntegrandt   NormalizeIntegrandAuxt   NormalizeIntegrandFactort   NormalizeIntegrandFactorBaset   NormalizeTogethert   NormalizeLeadTermSignst   AbsorbMinusSignt   NormalizeSumFactorst   SignOfFactort   NormalizePowerOfLineart   SimplifyIntegrandt   SimplifyTermt   TogetherSimplifyt   SmartSimplifyt   SubstForExpnt   ExpandToSumt   UnifySumt
   UnifyTermst	   UnifyTermt	   CalculusQt   FunctionOfInverseLineart   PureFunctionOfSinhQt   PureFunctionOfTanhQt   PureFunctionOfCoshQt   IntegerQuotientQt   OddQuotientQt   EvenQuotientQt   FindTrigFactort   FunctionOfSinhQt   FunctionOfCoshQt   OddHyperbolicPowerQt   FunctionOfTanhQt   FunctionOfTanhWeightt   FunctionOfHyperbolicQt   SmartNumeratort   SmartDenominatort   SubstForAuxt   ActivateTrigt
   ExpandTrigt
   TrigExpandt   SubstForTrigt   SubstForHyperbolict   InertTrigFreeQt   LCMt   SubstForFractionalPowerOfLineart   FractionalPowerOfLineart   InverseFunctionOfLineart
   InertTrigQt   InertReciprocalQt   DeactivateTrigt   FixInertTrigFunctiont   DeactivateTrigAuxt   PowerOfInertTrigSumQt   PiecewiseLinearQt   KnownTrigIntegrandQt   KnownSineIntegrandQt   KnownTangentIntegrandQt   KnownCotangentIntegrandQt   KnownSecantIntegrandQt   TryPureTanSubstt   TryTanhSubstt   TryPureTanhSubstt   AbsurdNumberGCDt   AbsurdNumberGCDListt   ExpandTrigExpandt   ExpandTrigReducet   ExpandTrigReduceAuxt   NormalizeTrigt	   TrigToExpt   ExpandTrigToExpt
   TrigReducet   FunctionOfTrigt   AlgebraicTrigFunctionQt   FunctionOfHyperbolict   FunctionOfQt   FunctionOfExpnQt   PureFunctionOfSinQt   PureFunctionOfCosQt   PureFunctionOfTanQt   PureFunctionOfCotQt   FunctionOfCosQt   FunctionOfSinQt   OddTrigPowerQt   FunctionOfTanQt   FunctionOfTanWeightt   FunctionOfTrigQt   FunctionOfDensePolynomialsQt   FunctionOfLogt   PowerVariableExpnt   PowerVariableDegreet   PowerVariableSubstt   EulerIntegrandQt   FunctionOfSquareRootOfQuadratict   SquareRootOfQuadraticSubstt   Dividest   EasyDQt   ProductOfLinearPowersQt   Rtt   NthRoott	   AtomBaseQt   SumBaseQt   NegSumBaseQt   AllNegTermQt   SomeNegTermQt   TrigSquareQt   RtAuxt
   TrigSquaret   IntSumt   IntTermt   Map2t   ConstantFactort   SameQt   ReplacePartt   CommonFactorst   MostMainFactorPositiont   FunctionOfExponentialQt   FunctionOfExponentialt   FunctionOfExponentialFunctiont    FunctionOfExponentialFunctionAuxt   FunctionOfExponentialTestt   FunctionOfExponentialTestAuxt   stdevt	   rubi_testt   Ift   IntQuadraticQt   IntBinomialQt   RectifyTangentt   RectifyCotangentt
   Inequalityt	   Conditiont   Simpt   SimpHelpt   SplitProductt   SplitSumt   SubstForRF  t   FresnelSt   FresnelCt   Erfct   Erfit   Gammat   FunctionOfTrigOfLinearQt   ElementaryFunctionQt   Complext   UnsameQt   _SimpFixFactort   SimpFixFactort   _FixSimplifyt   FixSimplifyt   _SimplifyAntiderivativeSumt   SimplifyAntiderivativeSumt   _SimplifyAntiderivativet   SimplifyAntiderivativet   _TrigSimplifyAuxt   TrigSimplifyAuxt   Cancelt   Partt   PolyLogt   Dt   Distt   Sum_doitt   PolynomialQuotientt   Floort   PolynomialRemaindert   FactorR  t   CosIntegralt   SinIntegralt   LogIntegralt   SinhIntegralt   CoshIntegralt   Rulet   Erft	   PolyGammat   ExpIntegralEit   ExpIntegralEt   LogGammat   UtilityOperatort	   Factorialt   Zetat
   ProductLogt   DerivativeDividest   HypergeometricPFQt   IntHidet   OneQt   Nullt   rubi_expt   rubi_logt   Discriminantt   Negativet   Quotient(   t   Integralt   St   sqrtt   Andt   Ort   Integert   Floatt   Modt   It   Abst   simplifyt   Mult   Addt   Powt   signt
   EulerGamma(   t   WC(   t   symbolst   Symbol(   t   sint   cost   tant   cott   csct   secR  t   erf(   t   acosht   asinht   atanht   acotht   acscht   asecht   cosht   sinht   tanht   cotht   secht   csch(   t   atant   acsct   asint   acott   acost   asect   atan2(   t   pit   ABCFGHabcdefghijklmnpqrtuvswxyzt   a1t   a2t   b1t   b2t   c1t   c2t   d1t   d2t   n1t   n2t   e1t   e2t   f1t   f2t   g1t   g2t   n3t   Pqt   Pmt   Pxt   Qmt   Qrt   Qxt   jnt   mnt   non2t   RFxt   RGxs   i ii Pqq Q R r C k uc     Z     s d d l  m } m } m } m } m } m } m } m } m	 }	 m
 }
 m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m  }  m! }! m" }" m# }# m$ }$ m% }% m& }& m' }' m( }( m) }) m* }* m+ }+ m, }, m- }- m. }. m/ }/ m0 }0 m1 }1 m2 }2 m3 }3 m4 }4 m5 }5 m6 }6 m7 }7 m8 }8 m9 }9 m: }: m; }; m< }< m= }= m> }> m? }? m@ }@ mA }A mB }B mC }C mD }D mE }E mF }F mG }G mH }H mI }I mJ }J mK }K mL }L mM }M mN }N mO }O mP }P mQ }Q mR }R mS }S mT }T mU }U mV }V mW }W mX }X mY }Y mZ }Z m[ }[ m\ }\ m] }] m^ }^ m_ }_ m` }` ma }a mb }b mc }c md }d me }e mf }f mg }g mh }h mi }i mj }j mk }k ml }l mm }m mn }n mo }o mp }p mq }q mr }r ms }s mt }t mu }u mv }v mw }w mx }x my }y mz }z m{ }{ m| }| m} }} m~ }~ m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } m } t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }   f d   } t | |  } t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }   f d   } t | |  } t t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }   f d   } t | |  } t t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }   f d   } t | |  } t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }   f d    } t | |  } t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  }   f d!   } t | |  } t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  }   f d"   } t | |  } t t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }   f d#   } t | |  } t t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }   f d$   } t | |  } t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | |	 |
 | |  }   f d%   } t | |  } t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | |	 |
 | |  }   f d&   } t | |  } t t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | |	 |
 | | | | 	 }   f d'   } t | |  }t t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | |	 |
 | | | | 	 }  f d(   }t || }t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }  f d)   }t || }t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }  f d*   }	t ||	 }
t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }  f d+   }t || }t t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }  f d,   }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }  f d-   }t || }t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }  f d.   }t || }t t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }  f d/   }t || }t t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }  f d0   }t || }t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }  f d1   }t || }t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }   f d2   }!t | |! }"t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }#  f d3   }$t |#|$ }%t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }&  f d4   }'t |&|' }(t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  })  f d5   }*t |)|* }+t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  },  f d6   }-t |,|- }.t t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }/  f d7   }0t |/|0 }1t t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }2  f d8   }3t |2|3 }4t t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t  | | |	 |
 | |  }5  f d9   }6t |5|6 }7t t t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t t t d t d   t d t d    t t d t d   t t t d t d   t d t d    t t  | | |	 |
 | | | | 	 }8  f d:   }9t |8|9 }:t t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t d
 t d   t d t d   t  | | |	 |
 | | | | 	 };  f d;   }<t |;|< }=t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }>  f d<   }?t |>|? }@t t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | |  }A  f d=   }Bt |A|B }Ct t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }D  f d>   }Et |D|E }Ft t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }G  f d?   }Ht |G|H }It t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }J  f d@   }Kt |J|K }Lt t t t d t d   t t t d t d   t d t d    t d t d   t d	 t d   t t t d t d   t d t d    t d
 t d   t  | | | | | | | | 	 }M  f dA   }Nt |M|N }Ot t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }P  f dB   }Qt |P|Q }Rt t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }S  f dC   }Tt |S|T }Ut t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }V  f dD   }Wt |V|W }Xt t t t d t d   t t t d t d   t d t d    t d t d   t  | | | | | |  }Y  f dE   }Zt |Y|Z }[t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }\  f dF   }]t |\|] }^t t t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t  | | | |	 |
 | |  }_  f dG   }`t |_|` }at t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }b  f dH   }ct |b|c }dt t t t t d t d   t t t d t d   t d t d    t  | | |	 |
 |  }e  f dI   }ft |e|f }gt t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }h  f dJ   }it |h|i }jt t t d t d   t t t d t d   t d t d    t d
 t d   t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 |
 | | | 	 }k  f dK   }lt |k|l }mt t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }n  f dL   }ot |n|o }pt t t d t d   t t t d t d   t d t d    t d
 t d   t t d t d   t t t d t d   t d t d    t d  t d t d   t  | | | |	 | | |  }q  f dM   }rt |q|r }st t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  }t  f dN   }ut |t|u }vt t t t d t d   t d t d   t t t d t d   t d t d    t d t d   t t t d t d   t d t d    t d  t  | | |	 |
 | |  }w  f dO   }xt |w|x }yt t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }z  f dP   }{t |z|{ }|t t t t t d t d   t t t d t d   t d t d    t d  t  | | |	 | |  }}  f dQ   }~t |}|~ }t t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t d
 t d   t d t d   t  | | |	 |
 | | | | 	 }  f dR   }t || }t t t t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t t d t d   t d  t t t d t d   t d t d    t d
 t d   t d t d   t  | | |	 |
 | | | | 	 }  f dS   }t || }t t t t t d t d   t d t d    t t t d	 t d   t d t d    t  | | | | |  }  f dT   }t || }t t t t t d t d   t d t d    t t t d	 t d   t d t d    t  | | | | |  }  f dU   }t || }t t t t t d t d   t d t d    t t t d	 t d   t d t d    t  | | | | |  }  f dV   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t d  t  | | | | | | | | 	 }  f dX   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t d  t  | | | | | | | | 	 }  f dY   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t t t d	 t d   t d t d    t d[ t d   t  | | | | | | | | | 
 }  f d\   }t || }t t t d] t d   t t t d t d   t d t d    t d
 t d   t t t d	 t d   t d t d    t d[ t d   t  | | | | | | | | | 
 }  f d^   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  }  f d_   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  }  f d`   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  }  f da   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  }  f db   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  |! |"  }  f dc   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |  |! |"  }  f dd   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |# |  |$ |% |"  }  f de   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |# |  |$ |% |"  }  f df   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |& |# |' |"  }  f dg   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |& |# |' |"  }  f dh   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |& |( |$ |) |"  }  f di   }t || }t t t dZ t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |& |( |$ |) |"  }  f dj   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |* |+ |,  }  f dk   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |* |+ |,  }  f dl   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |* |  |,  }  f dm   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | |* |  |,  }  f dn   }t || }t t t t t d t d   t d t d    t t t t d	 t d   t d t d     t  | | | | | |  }  f do   }t || }t t t t t d t d   t d t d    t t t t d	 t d   t d t d     t  | | | | | |  }  f dp   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | | |,  }  f dq   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t  | | | | | | | | | |,  }  f dr   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |  }  f ds   }t || }t t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |  }  f dt   }t || }t t t dW t d   t t t d	 t d   t d t d    t t t t d t d   t d t d    t d  t t t d t d   t d t d    t d  t  | | | | | | | | 	 }  f du   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t d] t d   t t t d t d   t d t d    t d
 t d   t t t d	 t d   t d t d    t d[ t d   t  | | | | | | | | | | |  }  f dv   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | | |-  }  f dw   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | | |-  }  f dx   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | | |. |)  }  f dy   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |/ |  |0 |1  }  f dz   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |/ |  |0 |1  }  f d{   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |# |  |2 |0 |1 |3  }  f d|   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |# |  |2 |0 |1 |3  }  f d}   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |4 |# |5 |0 |1  }  f d~   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | |4 |# |5 |0 |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |& |# |6 |1  }  f d   }t || } t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |& |# |6 |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |7 |( |8 |+ |6 |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |7 |( |8 |+ |6 |1  }  f d   }t || }	t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |7 |( |8 |  |2 |) |1  }
  f d   }t |
| }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | |7 |( |8 |  |2 |) |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |& |( |2 |) |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |& |( |2 |) |1  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t d] t d   t t t d t d   t d t d    t d
 t d   t dW t d   t t t d	 t d   t d t d    t t  | | | | | | | | | | | | |  }  f d   }t || }t t t dZ t d   t t t d t d   t d t d    t d t d   t t t d	 t d   t d t d    t  | | | | | | | |9 	 }  f d   }t || }t t t t t d	 t d   t d t d   t d t d   t t t  | | | | |: |; |<  }  f d   }t || }t t t d  t t t d	 t d   t d t d   t d t d   t t  | | | | |: |= |>  }  f d   } t ||  }!t t t d  t t t d	 t d   t d t d   t d t d   t t  | | | | |: |? |>  }"  f d   }#t |"|# }$t t t t t d	 t d   t d t d   t t t d	 t d   t d t d   t d t d   t t  | | | | | |@ |; |> 	 }%  f d   }&t |%|& }'  f d   }(t t t t t d	 t d   t d t d   t d t d   t t  | | | | | |: |A | 	 })t |)|( }*  f d   }+t t t t t d	 t d   t d t d   t d t d   t t d t d   t d
 t d   t  | | | | | | |: |A | 
 },t |,|+ }-d   }.t t t t t t d t d   t d t d   t d t d   t  | | | |B t |.  }/  f d   }0t |/|0 }1d   }2t t t t t t d t d   t d t d   t d t d   t  | | | |C t |2  }3  f d   }4t |3|4 }5d   }6t t t t t t d t d   t d t d   t d t d   t  | | | |D t |6  }7  f d   }8t |7|8 }9d   }:t t t t t t d t d   t d t d   t d t d   t  | | | |E t |:  };  f d   }<t |;|< }=d   }>t t t t t d t d   t d t d   t d t d   t t  | | | |F |G t |>  }?  f d   }@t |?|@ }Ad   }Bt t t t t t d t d   t d t d   t d t d    t d  t  | | | |F t |B  }C  f d   }Dt |C|D }Ed   }Ft t t t t d t d   t d t d   t d t d   t t  | | | |F |H t |F  }G  f d   }Ht |G|H }Id   }Jt t t t t t d t d   t d t d   t d t d    t d  t  | | | |F t |J  }K  f d   }Lt |K|L }Md   }Nt t t t t d t d   t d t d   t d t d   t t  | | | |; |D t |N  }O  f d   }Pt |O|P }Qd   }Rt t t t t d t d   t d t d   t d t d   t t  | | | |; |E t |R  }S  f d   }Tt |S|T }Ud   }Vt t t t  t |V  }W  f d   }Xt |W|X }Yd   }Zt t t t  t |Z  }[  f d   }\t |[|\ }]t t t t t d t d   t d t d   t t t d	 t d   t d t d   t  | | | | |I |J |K  }^  f d   }_t |^|_ }`t t t t t d t d   t d t d   t t t d	 t d   t d t d   t t t d] t d   t dZ t d   t  | | | | | | |I |J |L |M  }a  f d   }bt |a|b }cd   }dt t t t t t d t d   t d t d   t d t d   t  | | | |B t |d  }e  f d   }ft |e|f }gd   }ht t t t t t d t d   t d t d   t d t d   t  | | | |C t |h  }i  f d   }jt |i|j }kd   }lt t t t t t d t d   t d t d   t d t d   t  | | | |D t |l  }m  f d   }nt |m|n }od   }pt t t t t t d t d   t d t d   t d t d   t  | | | |E t |p  }q  f d   }rt |q|r }sd   }tt t t t t d t d   t d t d   t d t d   t t  | | | |? |F |B t |t  }u  f d   }vt |u|v }wd   }xt t t t t d t d   t d t d   t d t d   t t  | | | |? |F |G t |x  }y  f d   }zt |y|z }{d   }|t t t t t d t d   t d t d   t d t d   t t  | | | |? |F |C t ||  }}  f d   }~t |}|~ }d   }t t t t t d t d   t d t d   t d t d   t t  | | | |? |F |H t |  }  f d   }t || }d   }t t t t t d t d   t d t d   t d t d   t t  | | | |? |F |D t |  }  f d   }t || }d   }t t t t t d t d   t d t d   t d t d   t t  | | | |? |F |E t |  }  f d   }t || }d   }t t t t t t d t d   t d t d   t d t d   t d	 t d   t t  | | | | |N |? |F |B t | 
 }  f d   }t || }d   }t t t t t t d t d   t d t d   t d t d   t d	 t d   t t  | | | | |N |? |F |C t | 
 }  f d   }t || }d   }t t t t  t |  }  f d   }t || }d   }t t t t  t |  }  f d   }t || }t t t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t d[ t d   t d t d   t  | | | | | | |O  }  f d   }t || }t t t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t d[ t d   t d t d   t  | | | | | | |P  }  f d   }t || }t t t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t d[ t d   t d t d   t  | | | | | | |P  }  f d   }t || }d   }t t t t t  |Q t |  }  f d   }t || }d   }t t t t t t  |Q t |  }  f d   }t || }d   }t t t t t d t d   t  | |R |Q t |  }  f d   }t || }d   }t t t t t d t d   t t d
 t d   t  | | |R |Q t |  }  f d   }t || }  f d   }t t t t t d	 t d   t d t d   t d t d   t t d t d   t  | | | | | |: |A | 	 }t || }  f d   }t t t t t d	 t d   t d t d   t d t d   t t d t d   t d
 t d   t d t d   t  | | | | | | |: |A | 
 }t || }d   }t t t t  |S t |  }  f d   }t || }t t t d  t t t d	 t d   t d t d    t d
 t d   t d t d   t d t d   t t t d	 t d   t d t d    t d
 t d   t t d t d   t  | | | | |T  }  f d   }t || }t t t d  t t t d	 t d   t d t d    t d
 t d   t d t d   t d  t t t d	 t d   t d t d    t d
 t d   t d t d   t t d t d   t  | | | | |T  }  f d   }t || }t t t t t t d	 t d   t d t d   t t t t d	 t d   t d t d   t d t d   t d
 t d   t  | | | | | |V |: |; |U 
 }  f d   }t || }t t t t t t dZ t d   t d	 t d   t t t t dZ t d   t d	 t d   t d t d   t t t dZ t d   t d	 t d   t d t d   t d
 t d   t  | | | | | | |V |X |: |; |U |W  }  f d   }t || }t t t t t t dZ t d   t d	 t d   t d t d   t t t dZ t d   t d	 t d   t d t d   t t d
 t d   t  | | | | | | |V |: |; |Y  }  f d   }t || }t t t d t d   t t t d	 t d   t d t d    t d t d   t t t d	 t d   t d t d    t d
 t d   t d t d   t  | | | | | |Z  }  f d   }t || }t t t t  |[  }  f d   }t || }  f d   }t t t t t t d t d   t  | | | |\  }t || }  f d   }t t t t t t d t d   t  | | | |\  }t || }  f d   }t t t t d t d   t t d
 t d   t t d t d   t  | | | | |]  }t || }d   }t t t t  |Q t |  }  f d   }t || }d   }t t t t  |S |^ t |  }  f d   }t || }  f d   }t t t t  |Q  }t || }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t  | | | | | |_ |`  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t t t d t d   t d t d    t d
 t d   t  | | | | | |_ |`  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d[ t d   t  | | | | | |a  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d[ t d   t  | | | | | |a  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d[ t d   t t t d t d   t d t d    t d
 t d   t  | | | | | |a  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d[ t d   t  | | | | | |b |& |c 	 }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t d[ t d   t  | | | | | |b |& |c 	 }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d  t  | | | | | |_ |`  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d  t  | | | | | |_ |`  }   f d   }t | | }t t t t d	 t d   t d t d   t d t d   t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | |  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t t  | | | | | | |  }  f d   }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t t t t d t d   t d t d    t  | | | | | |  }	  f d   }
t |	|
 }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t t  | | | | | | |  }  f d   }t || }  f d   }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t t t d t d   t d t d    t d[ t d   t  | | | | | | |_ |d 	 }t || }  f d   }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t d[ t d   t  | | | | | | |_ |d 	 }t || }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t d
 t d   t  | | | | |& |;  }  f d   }t || }  f d   }t t t t d	 t d   t d t d   t d t d   t d  t t t d t d   t d t d    t d
 t d   t d  t t t d t d   t d t d    t d[ t d   t  | | | | |T |& |c |e 	 }t || }t t t t t t t t d t d   t  | | | |f |g |h |i |j 	 }  f d   }t || }t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t  | | | | | | | |_ |` 
 }  f d   }t || } t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t  | | | | | | | |_ |` 
 }!  f d   }"t |!|" }#t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t d  t  | | | | | | | |_ |` 
 }$  f d   }%t |$|% }&t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t d  t  | | | | | | | |_ |` 
 }'  f d   }(t |'|( })t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d	 t d   t d t d    t  | | | | | | | |_ |` 
 }*  f d   }+t |*|+ },t t t t d t d   t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d	 t d   t d t d    t  | | | | | | | |_ |` 
 }-  f d   }.t |-|. }/t t t t d] t d   t dZ t d   t d t d   t t t d t d   t d t d    t d[ t d   t t t d	 t d   t d t d    t d t d   t  | | | | | | |K |k 	 }0  f d   }1t |0|1 }2t t t t d] t d   t dZ t d   t d t d   t t t d t d   t d t d    t d[ t d   t t t d	 t d   t d t d    t d t d   t  | | | | | | |K |k 	 }3  f d   }4t |3|4 }5t t t t d] t d   t dZ t d   t d t d   t t t d t d   t d t d    t d[ t d   t t t d	 t d   t d t d    t d t d   t  | | | | | | | |K 	 }6  f d   }7t |6|7 }8t t t t t d t d   t d t d   t t t d	 t d   t d t d   t t d] t d   t dZ t d   t d t d   t  | | | | | | | |l |m |K | |n  }9  f d   }:t |9|: };t t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t  |p | | | | | |o  }<  f d  }=t |<|= }>t t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t  |p | | | | | |o  }?  f d  }@t |?|@ }At t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | |q |r |s 
 }B  f d  }Ct |B|C }Dt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | |t |& |# 
 }E  f d  }Ft |E|F }Gt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | | |u |` |v  }H  f d  }It |H|I }Jt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | | |u |` |v  }K  f d  }Lt |K|L }Mt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | |w |r |5 |x  }N  f d  }Ot |N|O }Pt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | |w |r |5 |x  }Q  f d  }Rt |Q|R }St t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | | |A 	 }T  f d	  }Ut |T|U }Vt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t t  |p | | | | | | |A 	 }W  f d
  }Xt |W|X }Yt t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |;  }Z  f d  }[t |Z|[ }\t t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |;  }]  f d  }^t |]|^ }_t t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | |q |r |5 
 }`  f d  }at |`|a }bt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | |q |r |5 
 }c  f d  }dt |c|d }et t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | | |y |z |{  }f  f d  }gt |f|g }ht t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | | |y |z |{  }i  f d  }jt |i|j }kt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | || |r |s |}  }l  f d  }mt |l|m }nt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t t  |p | | | | | || |r |s |}  }o  f d  }pt |o|p }qt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |;  }r  f d  }st |r|s }tt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |;  }u  f d  }vt |u|v }wt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |A  }x  f d  }yt |x|y }zt t t t t d t d   t d t d   t d t d   t d  t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |A  }{  f d  }|t |{|| }}t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | | | |~ |  }~  f d  }t |~| }t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | | | | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | | | | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t t t dZ t d   t d	 t d    t d t d   t  |p | | | | | | | |~ | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t t t dZ t d   t d	 t d    t d t d   t  |p | | | | | | | | | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dW t d   t t t dZ t d   t d	 t d    t d
 t d   t t t dZ t d   t d	 t d    t d t d   t  |p | | | | | | | | | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dt d   t t t dZ t d   t d	 t d    t t dW t d   t t t dZ t d   t d	 t d    t  |p | | | | | | | | | |~ | |  }  f d  }t || }t t t t t d t d   t d t d   t d t d   t t dt d   t t t dZ t d   t d	 t d    t t dW t d   t t t dZ t d   t d	 t d    t  |p | | | | | | | | | |~ | |  }  f d  }t || }t t t t t d t d   t t t  |p | | |g | |  }  f d   }t || }  f d!  }t t t t t d t d   t d t d   t d t d   t t d t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |& |c | 
 }t || }  f d"  }t t t t t d t d   t d t d   t d t d   t t d t d   t t t dZ t d   t d	 t d    t d
 t d   t  |p | | | | | |& |c | 
 }t || }t t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t d t d   t t t dW t d   t d] t d    t d
 t d   t  |p | | | | | | | | 
 }  f d#  }t || }t t t t t d t d   t d t d   t d t d   t t d[ t d   t t t dZ t d   t d	 t d    t d t d   t t t dW t d   t d] t d    t d
 t d   t  |p | | | | | | | | 
 }  f d$  }t || }t t t t t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d   t t t dZ t d   t d	 t d   t  |p | | | | | | |g | 
 }  f d%  }t || }t t t t t t  t d
 t d   t  |p | | |  }  f d&  }t || }t t t t t t  t d
 t d   t  |p | | |  }  f d'  }t || }t t t t t t  t d t d   t t  t d
 t d   t  |p | | |  }  f d(  }t || }t t t t d t d   t d t d   t t t d
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 t d   t d t d     t d[ t d   t  | | | | |< |  }  f d+  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | |< |  }  f d,  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | |  }  f d-  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | |  }  f d.  }t || }t t t t d t d   t d t d   t t t d
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 t d   t d t d     t t  | | | | |* |  | | 	 }  f d1  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | |* |  | | 	 }  f d2  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |  }  f d3  }t || }t t t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |  }  f d4  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | | | |R 
 }  f d5  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | | | |R 
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 t d   t d t d     t d[ t d   t  | | | | | |< |  }  f d7  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | | |< |  }  f d8  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | | |  }  f d9  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | | |  }  f d:  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* | | 	 }  f d;  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* | | 	 }  f d<  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* |  | | 
 }  f d=  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* |  | | 
 }  f d>  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | |  }  f d?  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | |  }  f d@  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | |  }  f dA  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | |  }  f dB  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | |  }  f dC  } t ||  }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | |  }  f dD  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | |* | | | 	 }  f dE  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | |* | | | 	 }  f dF  }	t ||	 }
t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | |* |  |  }  f dG  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | |* |  |  }  f dH  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | | |  }  f dI  }t || }t t t d  t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | | |  }  f dJ  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | | |  }  f dK  }t || }t t t t d t d   t t d t d   t d t d   t t t d
 t d   t d t d     t  | | | | | |  }  f dL  }t || }t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | | |R | 
 }  f dM  }t || }t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | | | |R | 
 }   f dN  }!t | |! }"t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* | | | 
 }#  f dO  }$t |#|$ }%t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* | | | 
 }&  f dP  }'t |&|' }(t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* |  | 	 })  f dQ  }*t |)|* }+t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t t  | | | | | |* |  | 	 },  f dR  }-t |,|- }.t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | | | |  }/  f dS  }0t |/|0 }1t t t t d t d   t d  t t d t d   t d t d   t t t d
 t d   t d t d     t d[ t d   t  | | | | | | |  }2  f dT  }3t |2|3 }4t t t t t d t d    t d[ t d   t t t d t d   t t t d t d    t d[ t d    t  | | |* |+  }5  f dU  }6t |5|6 }7t t t t t d t d    t d[ t d   t t t d t d   t t t d t d    t d[ t d    t  | | |* |+  }8  f dV  }9t |8|9 }:t t t t t d t d    t d[ t d   t t t t d t d   t t t d t d    t d[ t d    t  | | | |+  };  f dW  }<t |;|< }=t t t t t d t d    t d[ t d   t t t t d t d   t t t d t d    t d[ t d    t  | | | |+  }>  f dX  }?t |>|? }@t t t t d t d   t t t d t d    t d[ t d   t t t d
 t d   t d t d   t t t d t d    t d[ t d    t  | | | | | |* |+  }A  f dY  }Bt |A|B }Ct t t t d t d   t t t d t d    t d[ t d   t t t d
 t d   t d t d   t t t d t d    t d[ t d    t  | | | | | |* |+  }D  f dZ  }Et |D|E }Ft t t t d t d   t t t d t d    t d[ t d   t t t d
 t d   t d t d   t t t d t d    t d[ t d    t  | | | | |* |+ |  }G  f d[  }Ht |G|H }It t t t t t t d t d    t d[ t d   t t t d
 t d   t d t d   t t t d t d    t d[ t d    t  | | | | |* |+ |  }J  f d\  }Kt |J|K }Lt t t t d t d   t t d	 t d   t d t d    t d
 t d   t  | | | |  }M  f d]  }Nt |M|N }Ot t t t d t d   t t d	 t d   t d t d    t d
 t d   t  | | | |  }P  f d^  }Qt |P|Q }Rt t t t t d t d   t d t d   t dZ t d   t t d	 t d   t d t d    t d
 t d   t  | | | | | |  }S  f d_  }Tt |S|T }Ut t t t t d t d   t d t d   t dZ t d   t t d	 t d   t d t d    t d
 t d   t  | | | | | |  }V  f d`  }Wt |V|W }X  f da  }Yt t t t  t d
 t d   t  | |  }Zt |Z|Y }[  f db  }\t t t t  t d
 t d   t  | |  }]t |]|\ }^t t t d t d   t t  t d[ t d   t t  t d t d   t  |h  }_  f dc  }`t |_|` }at t t d t d   t t  t d[ t d   t t  t d t d   t  |h  }b  f dd  }ct |b|c }dt t t t  t d[ t d   t t  t d t d   t  | |K  }e  f de  }ft |e|f }gt t t t  t d[ t d   t t  t d t d   t  | |K  }h  f df  }it |h|i }jt t t t d t d   t t  t d[ t d   t t  t d t d   t  | |  }k  f dg  }lt |k|l }mt t t t d t d   t t  t d[ t d   t t  t d t d   t  | |  }n  f dh  }ot |n|o }pt t t d t d   t t  t d[ t d   t t  t d[ t d   t  |h |  }q  f di  }rt |q|r }st t t t  t d[ t d   t t  t d t d   t  |K |  }t  f dj  }ut |t|u }vt t t t d t d   t t  t d[ t d   t t  t d t d   t  | |  }w  f dk  }xt |w|x }yt t t t  t t  t d
 t d   t  |r |8 |  }z  f dl  }{t |z|{ }|t t t d  t t  t d
 t d   t t  t  |r |8 |  }}  f dm  }~t |}|~ }t t t d  t t  t d
 t d   t t  t  |r |8 |  }  f dn  }t || }t t t t  t t  t d
 t d   t  |r |8 |  }  f do  }t || }t t t d  t t  t d
 t d   t t  t  |r |8 |  }  f dp  }t || }t t t d  t t  t d
 t d   t t  t  |r |8 |  }  f dq  }t || }t t t d  t t  t d
 t d   t t  t  |r |8 |  }  f dr  }t || }t t t d  t t  t d
 t d   t t  t  |r |8 |  }  f ds  }t || }t t t t d t d   t t t d	 t d   t d t d    t t t d	 t d   t d t d    t d
 t d   t t d] t d   t dZ t d   t d t d   t  | | | | | | | | | 
 }  f dt  }t || }t t t t d t d   t t d t d   t t t d	 t d   t d t d    t d  t t  | | | | | | |c | | 
 }  f du  }t || }t t t t d t d   t t d t d   t t t d	 t d   t d t d    t d  t t  | | | | | | |c | | 
 }  f dv  }t || }t t t t d] t d   t dZ t d   t d t d   t t t t d	 t d   t t d t d   t d t d    t d[ t d   t  | | | | | | | |_ |* 
 }  f dw  }t || }t t t t d] t d   t dZ t d   t d t d   t t t t d	 t d   t t d t d   t d t d    t d[ t d   t  | | | | | | | |_ |* 
 }  f dx  }t || }t t t t dW t d   t d] t d   t d t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t  | | | | | | | |_ | |  }  f dy  }t || }t t t t dW t d   t d] t d   t d t d   t t d t d   t t t dZ t d   t d	 t d    t d  t t t dZ t d   t d	 t d    t d  t  | | | | | | |_  }  f dz  }t || }t t t t dW t d   t d] t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t t t dZ t d   t d	 t d    t d  t  | | | | | | | |_ | |  }  f d{  }t || }t t t t dW t d   t d] t d   t d t d   t t d t d   t t t dZ t d   t d	 t d    t d  t t t dZ t d   t d	 t d    t d  t  | | | | | | |_  }  f d|  }t || }t t t t dW t d   t d] t d   t d t d   t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t d t d   t t t dZ t d   t d	 t d    t d  t  | | | | | | | |_ | |  }  f d}  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ | 	 }  f d~  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ | 	 }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ | 	 }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ | 	 }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ |; |s |  }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ |; |s |  }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ |; |s |  }  f d  }t || }t t t t d] t d   t dZ t d   t d t d   t t t d	 t d   t d t d    t t t d t d   t t t d	 t d   t d t d    t  | | | | | | |_ |; |s |  }  f d  }t || }t t t t d t d   t t t d	 t d   t d t d    t t d] t d   t dZ t d   t t d t d   t t t d	 t d   t d t d    t d  t  | | | | | | |	 |
 | 
 }  f d  }t || }t t t t d t d   t t t d	 t d   t d t d    t t d] t d   t dZ t d   t t d t d   t t t d	 t d   t d t d    t d  t  | | | | | | |	 |
 | 
 }  f d  }t || }t t t t d t d   t t  t d
 t d   t d  t t  t d t d   t  | | | | |  }  f d  }t || }t t t t d t d   t t  t d
 t d   t d  t t  t d t d   t  | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t t d	 t d   t d t d    t d
 t d   t  | | | | |  }  f d  }t || }t t t d t d   t t t d t d   t d t d    t d t d   t t t d	 t d   t d t d    t d
 t d   t  | | | | |  }  f d  }t || }t t t d  t t t t d	 t d    t t t d t d   t d t d    t  | | | | | |  }  f d  }t || }t t t d  t t t t d	 t d    t t t d t d   t d t d    t  | | | | | |  }  f d  }t || }t t t t t t d	 t d    t t t d t d   t d t d    t  | | | | | |  }  f d  }t || }t t t d  t t t t d	 t d    t t t d t d   t d t d    t  | | | | | |  }  f d  }t || }t t t d t d   t t  t d t d   t t  t d
 t d   t d t d   t  | | | |Z  }  f d  }t || }| | | | | | | | | | | | | | | | | | | | | | | ||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y|||||||||||||||||||||||||||||||||||||||||||||| |||	||||||||!|$|'|*|-|1|5|9|=|A|E|I|M|Q|U|Y|]|`|c|g|k|o|s|w|{|||||||||||||||||||||||||||||||||||||||||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||||||||||||||||||||||||||||||
||||||||"|%|(|+|.|1|4|7|:|=|@|C|F|I|L|O|R|U|X|[|^|a|d|g|j|m|p|s|v|y||||||||||||||||||||||||||||||||||||||gZS(  Ni(   t   cons1646t   cons18t   cons2t   cons3t   cons7t   cons27t   cons21t   cons4t   cons34t   cons35t   cons36t   cons1647t   cons1648t   cons1649t   cons1650t   cons1651t   cons1652t   cons1653t   cons25t   cons1654t   cons1408t   cons208t   cons38t   cons48t   cons125t   cons147t   cons343t   cons5t   cons240t   cons244t   cons1333t   cons137t   cons1655t   cons1288t   cons166t   cons319t   cons1656t   cons31t   cons249t   cons94t   cons253t   cons13t   cons163t   cons246t   cons1278t   cons1657t   cons1658t   cons1659t   cons170t   cons1660t   cons1661t   cons93t   cons89t   cons1662t   cons162t   cons88t   cons1663t   cons1664t   cons85t   cons128t   cons1479t   cons744t   cons1482t   cons1665t   cons23t   cons1666t   cons1667t   cons1668t   cons1669t   cons1247t   cons1670t   cons1671t   cons1672t   cons1673t   cons555t   cons1674t   cons628t   cons10t   cons1675t   cons1676t   cons1677t   cons66t   cons1230t   cons376t   cons49t   cons50t   cons51t   cons52t   cons1678t   cons1439t   cons1679t   cons1680t   cons1681t   cons1682t   cons62t   cons584t   cons464t   cons1683t   cons168t   cons1684t   cons1685t   cons1686t   cons1687t   cons1688t   cons812t   cons813t   cons17t   cons1689t   cons1690t   cons1691t   cons1692t   cons1099t   cons1693t   cons87t   cons165t   cons1694t   cons1695t   cons1395t   cons1696t   cons1442t   cons1697t   cons1502t   cons963t   cons1698t   cons1644t   cons1699t   cons196t   cons1700t   cons1011t   cons150t   cons1551t   cons1701t   cons1702t   cons209t   cons224t   cons1703t   cons810t   cons811t   cons148t   cons528t   cons1704t   cons1705t   cons1706t   cons1707t   cons1708t   cons54t   cons1709t   cons1710t   cons146t   cons1711t   cons1505t   cons1712t   cons1713t   cons1714t   cons1715t   cons1716t   cons1717t   cons1718t   cons1719t   cons1645t   cons1720t   cons1721t   cons1722t   cons1723t   cons1724t   cons338t   cons53t   cons627t   cons71t   cons1725t   cons1726t   cons1727t   cons1728t   cons1360t   cons1478t   cons463t   cons1729t   cons1730t   cons1731t   cons1732t   cons1265t   cons1267t   cons1474t   cons1481t   cons1733t   ci   t   bt   ai    t   mt   dt   nc      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | | t | | |  | t |   |  |  S(   NiM  (   t   appendR  R  R  R  R   RG  (   t   uR  R  R  R  R  R  t   x(   t   rubi(    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4685   s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | | t |   |  |  S(   NiN  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4686   s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | | t | | |  | t |   |  |  S(   NiO  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4687   s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | | t |   |  |  S(   NiP  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4688   s    c            s{     j  d  t | t | | |  | | t | | |  | t | t | | |  | | t |   |  |  S(   NiQ  (   R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4689   s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | t |   |  |  S(   NiR  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4690   s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | t |   |  |  S(   NiS  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4691   s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   NiT  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4692   s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   NiU  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4693   s    t   Bc      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   NiV  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  t   A(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4694   s    c      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   NiW  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4695   s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   NiX  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4696   s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   NiY  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4697   s    R  t   Ci   R  c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   NiZ  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4698   s    c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   Ni[  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4699   s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Ni\  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4700   s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Ni]  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4701   s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Ni^  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4702   s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Ni_  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4703   s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Ni`  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4704   s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Nia  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4705   s    c            sl     j  d  t | t | | |  |  t | | |  t d  | t |  t | | |  |  S(   Nib  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4706   s    c            sl     j  d  t | t | | |  |  t | | |  t d  | t |  t | | |  |  S(   Nic  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4707   s    c
   
         sp     j  d  t |	 |  t | | |  | t | | |  t d  t |  t | | |  | |  S(   Nid  i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4708  s    c
   
         sp     j  d  t |	 |  t | | |  | t | | |  t d  t |  t | | |  | |  S(   Nie  i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4709  s    c            s{     j  d  t | t | | |  | | t | | |  | t | t | | |  | | t |   |  |  S(   Nif  (   R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4710  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | | t |   |  |  S(   Nig  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4711  s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   Nih  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4712  s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   Nii  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4713  s    c      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   Nij  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4714   s    c      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   Nik  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4715%  s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   Nil  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4716*  s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   Nim  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4717/  s    c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   Nin  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement47184  s    c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   Nio  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement47199  s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Nip  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4720>  s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Niq  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4721C  s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Nir  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4722H  s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Nis  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4723M  s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Nit  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4724R  s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Niu  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4725W  s    c            sl     j  d  t | t | | |  |  t | | |  t d  | t |  t | | |  |  S(   Niv  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4726\  s    c
   
         sp     j  d  t |	 |  t | | |  | t | | |  t d  t |  t | | |  | |  S(   Niw  i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4727a  s    c
   
         sz     j  d  t |	 |  t | | |  | t | | |  t d  t d  t | | |  | t |  |  S(   Nix  i   i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4728f  s    c            s{     j  d  t | t | | |  | | t | | |  | t | t | | |  | | t |   |  |  S(   Niy  (   R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4729k  s    c            s{     j  d  t | t | | |  | | t | | |  | t | t | | |  | | t |   |  |  S(   Niz  (   R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4730p  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | | t |   |  |  S(   Ni{  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4731u  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | | t | | |  | t |   |  |  S(   Ni|  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4732z  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | | t |   |  |  S(   Ni}  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4733  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | | t | | |  | t |   |  |  S(   Ni~  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4734  s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   Ni  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4735  s    c            sw     j  d  t | t | | |  | | t | | |  | t | t | | |  | t |   |  |  S(   Ni  (   R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4736  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | t |   |  |  S(   Ni  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4737  s    c      	      s     j  d  t | t | | |  | | t | | |  | | t | | |  | t | t | | |  | | t | | |  | t |   |  |  S(   Ni  (   R  R  R  R  R  R   RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4738  s    c      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   Ni  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4739  s    c      	      sj     j  d  t | t | t | | |  | t d  | t | | |  |  t |  |  |  S(   Ni  i(   R  R  R   R  R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4740  s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   Ni  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4741  s    c            sL     j  d  t | t | | |  |  t |  t | | |  |  S(   Ni  (   R  R   R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4742  s    c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   Ni  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4743  s    c	   	   
      s     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t | | |  | t |  |  |  S(   Ni  i   i(   R  R  R  R   R  RG  (	   R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4744  s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Ni  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4745  s    c      	      s~     j  d  t | t d  t | t | | |  | t d  | t | | |  t d  |  t |  |  |  S(   Ni  i   i(   R  R  R  R   R  RG  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4746  s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Ni  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4747  s    c            sv     j  d  t | t | | |  t d  |  t | | |  | t |  t | | |  t d  |  S(   Ni  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4748  s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Ni  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4749  s    c            s`     j  d  t | t | | |  t d  |  t |  t | | |  t d  |  S(   Ni  i   (   R  R   R  R  RG  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4750  s    c
   
         sz     j  d  t |	 |  t | | |  | t | | |  t d  t d  t | | |  | t |  |  S(   Ni  i   i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4751  s    c
   
         sz     j  d  t |	 |  t | | |  | t | | |  t d  t d  t | | |  | t |  |  S(   Ni  i   i   (   R  R   R  R  RG  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4752  s    c            s     j  d  t t | | | |  |  t d  |  t d  | |  t t | | | |  |  t d  |  t d  | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4753  s    c            s     j  d  t t | | | |  |  t d  |  t d  | |  t t | | | |  |  t d  |  t d  | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4754  s    c            s     j  d  t t | | | |  |  t d  |  t d  | |  t t | | | |  |  t d  |  t d  | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4755  s    t   gc      	      s     j  d  t t d  d t | t | | |  |  |  |  t t d  d t | t | | |  |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   t   pR7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4756  s    c      	      s     j  d  t t d  d t | t | | |  |  |  |  t t d  d t | t | | |  |  t | | |  |  |  S(   Ni  i   i   (   R  R  R  R   R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4757  s    t   eR8  c            si     j  d  t t d  |  | |  t | t | | |  | |  t | | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R8  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4758  s    t   fc            si     j  d  t t d  |  | |  t | t | | |  | |  t | | |  |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R8  R=  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4759  s    c	   	         s     j  d  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   ii   (   R  R  R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4760  s    c	   	         s     j  d  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   ii   (   R  R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4761  s    c	   	         sa     j  d  t | t | | |  | | t | | |  |  t d  | | | |  S(   Ni  i   (   R  R  R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4762  s    c	   	         s`     j  d  t | t | | |  | | t | | |  |  t d  | | | |  S(   Ni  i   (   R  R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4763  s    c	   	   	      s+    j  d  t | t d  | |  t d  t d  | t d  |  t d  t | t | | |  | t d  | t | | |  |  t d  |  |  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   ii   i   ii(   R  R  R  R   R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4764  s    c	   	   	      s+    j  d  t | t d  | |  t d  t d  | t d  |  t d  t | t | | |  | t d  | t | | |  |  t d  |  |  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   ii   i   ii(   R  R  R  R   R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4765  s    c	   	   	      s    j  d  t | t d  | t d  |  t d  t d  | t d  |  t d  t | t | | |  | t d  | t | | |  |  t d  |  |  t | t | | |  | | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4766$  s    c	   	   	      s    j  d  t | t d  | t d  |  t d  t d  | t d  |  t d  t | t | | |  | t d  | t | | |  |  t d  |  |  t | t | | |  | | t | | |  |  t d  t d  | | |  t d  |  S(   Ni  i   i   i   i(   R  R  R  R   R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4767)  s    c	   	   	      s    j  d  t | t d  | |  t d  | t d  |  t | t | | |  | t d  | t | | |  |  |  |  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | | t d  |  |  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4768.  s    c	   	   	      s    j  d  t | t d  | |  t d  | t d  |  t | t | | |  | t d  | t | | |  |  |  |  t | t d  | t | | |  | t d  | t | | |  |  t d  t d  | | | t d  |  |  S(   Ni  i   iii   (   R  R  R  R   R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement47693  s    c	   	   	      s    j  d  t | t d  |  t d  | t d  | |  t d  t | t | | |  | t d  | t | | |  |  |  |  t | t | | |  | | t | | |  |  t d  t d  | | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement47708  s    c	   	   	      s    j  d  t | t d  |  t d  | t d  | |  t d  t | t | | |  | t d  | t | | |  |  |  |  t | t | | |  | | t | | |  |  t d  t d  | | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4771=  s    c            s     j  d  t t d  | |  t d  |  t d  t | t | | |  |  t d  t | | |  |  |  t t d  | t | | |  |  t | | |  | t d  |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4772B  s    c            s     j  d  t t d  | |  t d  |  t d  t | t | | |  |  t d  t | | |  |  |  t t d  | t | | |  |  t | | |  | t d  |  t d  |  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4773G  s    c            s     j  d  t t d  |  t d  t d  | |  t d  t | t | | |  |  t d  t | | |  |  |  t | t | | |  |  t d  t | | |  t d  | | |  t d  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4774L  s    c            s     j  d  t t d  |  t d  t d  | |  t d  t | t | | |  |  t d  t | | |  |  |  t | t | | |  |  t d  t | | |  t d  | | |  t d  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4775Q  s    c            s     j  d  t t t | |  |  t t | | |   t | |  |   | |  t t t | |  |  t | |  |   | |  S(   Ni  (   R  R  t   logR  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4776V  s    c            s     j  d  t t t | |  |  t t | | |   t | |  |   | |  t t t | |  |  t | |  |   | |  S(   Ni  (   R  R  RO  R  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4777[  s    c            sb     j  d  t t d  | t | t | | |  |  t d  t | | |  |  |  S(   Ni  i   i(   R  R  R  R   R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4778`  s    c            sb     j  d  t t d  | t | t | | |  |  t d  t | | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4779e  s    c	   	         s     j  d  t | t | | |  |  | t | | |  |  t | | |  |  t | t | | |  | |  t | | |  |  |  |  S(   Ni  (   R  R  R  R  R   (	   R8  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4780j  s    c	   	         s     j  d  t | t | | |  |  | t | | |  |  t | | |  |  t | t | | |  | |  t | | |  |  |  |  S(   Ni  (   R  R  R  R  R   (	   R8  R7  R=  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4781o  s    c      	      s     j  d  t t d  d t | t | | |  |  |  |  t t d  d t | t | | |  |  t | | |  t d  |  |  S(   Ni  i   i   i   (   R  R  R  R   R  R  (   R8  R7  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4782t  s    c
   
   	      sz     j  d  t t d  |  |	 |  | |  t |	 t | | |  | |  | t | | |  | |  |  |  S(   Ni  i   (   R  R  R  R   R  R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4783y  s    c            s     j  d  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | |  t d  |	  S(   Ni  ii   (   R  R  R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4784~  s    c            s     j  d  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | |  t d  |	  S(   Ni  ii   (   R  R  R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4785  s    c            s     j  d  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | |  t d  |	  S(   Ni  i   (   R  R  R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4786  s    c      	      sg    j  d  t |
 t d  | |  t d  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  |	  |	  t |
 t d  |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  t d  | | | |  t d  |	  S(   Ni  i   ii   i   ii(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4787  s    c      	      sg    j  d  t |
 t d  | |  t d  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  |	  |	  t |
 t d  |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  t d  | | | |  t d  |	  S(   Ni  i   ii   i   ii(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4788  s    c      	      s]    j  d  t |
 t d  | | t d  |  t d  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  |	  |	  t |
 t | | |	  | | t | | |	  | | t | | |	  |  t d  t d  | | | |  t d  |	  S(   Ni  i   i   i   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4789  s    c      	      s]    j  d  t |
 t d  | | t d  |  t d  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  t d  |	  |	  t |
 t | | |	  | | t | | |	  | | t | | |	  |  t d  t d  | | | |  t d  |	  S(   Ni  i   i   i   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4790  s    c      	      sI    j  d  t |
 t d  | |  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  |	  |	  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | |  t d  |	  S(   Ni  i   ii   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4791  s    c      	      sI    j  d  t |
 t d  | |  t d  | t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  |	  |	  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | |  t d  |	  S(   Ni  i   ii   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4792  s    c      	      s9    j  d  t |
 t d  | |  t d  | | t d  |  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  |	  |	  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | | t d  |  |	  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4793  s    c      	      s9    j  d  t |
 t d  | |  t d  | | t d  |  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  |	  |	  t |
 |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | | | | t d  |  |	  S(   Ni  i   iii   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4794  s    c      	      sU    j  d  t t d  | | | |  t d  |
 | | t d  |  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  t d  |	  |	  t | |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | t d  |  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4795  s    c      	      sU    j  d  t t d  | | | |  t d  |
 | | t d  |  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  t d  |	  |	  t | |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | t d  |  |	  S(   Ni  i   ii   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4796  s    c      	      s[    j  d  t | | | t d  |  t d  t d  |
 | | |  t d  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  t d  |	  |	  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | |  t d  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4797  s    c      	      s[    j  d  t | | | t d  |  t d  t d  |
 | | |  t d  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  t d  |	  |	  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | |  t d  |	  S(   Ni  i   i   i(   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4798  s    c      	      s?    j  d  t | | t d  |  t d  |
 t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  |	  |	  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | |  t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4799  s    c      	      s?    j  d  t | | t d  |  t d  |
 t d  | |  t d  t |
 t | | |	  | t d  | t | | |	  | | t | | |	  |  |	  |	  t |
 t | | |	  | t d  | t | | |	  | t d  | t | | |	  |  | |
 | | |  t d  |	  S(   Ni  i   i   (   R  R  R  R   R  R  R  (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4800  s    c      	      s     j  d  t |
 t | | |	  |  | t | | |	  |  | t | | |	  |  t |
 t | | |	  | |  | t | | |	  | |  |	  |	  S(   Ni  (   R  R  R  R  R   (   R8  R  R=  R  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4801  s    c            s     j  d  t | t | | |  |  t d  |  t d  t | | | |  t d   | | |  t d  |  S(   Ni  i   i   (   R  R  R  R  (   R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4802  s    c            s8     j  d  t | | | | | |  | |  |  S(   Ni  (   R  R   (   R8  R  R  R  R  R  R  t   F(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4803  s    c            s     j  d  t t d  | | t t t d  t d  t d  t d  t | | | | |  t d  t | |  | t d   |  t t t d  | t d    |  S(   Ni  i   i   ii   (   R  R  R  R  R   t   kR  R   (   R  R  R  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4804  s    c      	      sG     j  d  t t t d  | |  | | | |  | |  |  S(   Ni  i   (   R  R   RH  R  (   R  R  R  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4805  s    c	   	   
      s\     j  d  t t | | | |  |  t d  | | | | | |  | |  |  S(   Ni  i   (   R  R   RH  R  (	   R  R  t   GR  R  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4806  s    c            s   t  | | | |   }   j d  t | t |  | | |  t |  | t | |  |  t |  t | |  |  t |  t t | |  | |  |  |  S(   Ni  (   RG  R  R  R$   R%   R   R   (   R8  R  R  R  R  R  Rk  t   v(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4807  s    c   	         s   t  | | | |   }   j d  t | t |  | | | |  t |  | | |  t |  t | | | |  |  |  S(   Ni  (   RG  R  R  R$   R%   R   (	   R8  R  R  R  R  R  R  Rk  Rr  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4808  s    c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   t
   isinstancet   intR  t   floatR  t   FalseR   R  Rl  t   True(   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4809  s    !+c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4809  s    !c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4810
  s    !+c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4810  s    !c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4811  s    !+c            s   t  t | | | |  |  }   j d  t t d  | | t t t t d  | t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4811   s    !c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4812&  s    !+c            s   t  t | | | |  |  }   j d  t t d  | | t t t t d  | t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4812.  s    !c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With48134  s    !+c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4813<  s    !c         S   ss   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  | t	  ro t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4814B  s    !+c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4814J  s    !c         S   s   t  | t t t t f  r t St t d  t | | | |  |  } t	 t d  | t | | | |  |  | t
  r t
 St S(   Ni   (   Ru  Rv  R  Rw  R  Rx  R   R  R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4815P  s    +5c            s   t  t d  t | | | |  |  }   j d  t | | | t t t t d  t d  | t | | | |  |  |  |  | t d  | t | | | |   |  S(   Ni   i  (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4815X  s    +c         S   s   t  | t t t t f  r t St t d  t | | | |  |  } t	 t d  | t | | | |  |  | t
  r t
 St S(   Ni   (   Ru  Rv  R  Rw  R  Rx  R   R  R  Rl  Ry  (   R  R  R  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4816^  s    +5c            s   t  t d  t | | | |  |  }   j d  t | | | t t t t d  t d  | t | | | |  |  |  |  | t d  | t | | | |   |  S(   Ni   i  (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4816f  s    +c      	   S   s   t  | t t t t f  r t St t | | | |  |  } t t	 t | | | |  | |  | t
  t t d  t | | | |  | t |   |   r t
 St S(   Ni   (   Ru  Rv  R  Rw  R  Rx  R   R  R  Rl  Ry  R]  R  RG  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4817l  s    !gc            s   t  t | | | |  |  }   j d  t | | t d  | | t t t | | | t d  | t d  t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4817t  s    !c      	   S   s   t  | t t t t f  r t St t d  t | | | |  |  } t	 t
 t d  | t | | | |  |  | t  t t |   t | | | |  | |   r t St S(   Ni   (   Ru  Rv  R  Rw  R  Rx  R   R  R  R  Rl  Ry  R]  RG  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4818z  s    +gc            s   t  t d  t | | | |  |  }   j d  t | | t d  | | t t t | | | t d  | t d  t d  t d  | t | | | |  |  |  |  | t d  | t | | | |   |  S(   Ni   i  i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4818  s    +c         S   s   t  |  t t t t f  r t Sy t | |   } t t d  t	 |  |   } t
 t t |   t t t d  t	 |  |   | |  t  t t |  |    } Wn t t f k
 r t SX| r t St S(   Ni   (   Ru  Rv  R  Rw  R  Rx  Ri  R   R  R  R  R5   R   Rl  R   Ry  R]  RG  t	   TypeErrort   AttributeError(   R  R  Rr  R  t   res(    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4819  s    Yc            s  t  | |   } t t d  t |  |   }   j d  t t t t | t t d  t |  |     t	 | t
 | |  t d   t t t t d  | t d  |  t d  t d  t d  | t |  | |   |   |  t d  | t |   |    |   S(   Ni   i  i   (   Ri  R   R  R  R  R  R
   R   R	   R  R2   R*   R   R  (   R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4819  s    c         S   s   t  |  t t t t f  r t Sys t | |   } t t |  |   } t	 t
 t |   t t t |  |   | |  t  t t |  |    } Wn t t f k
 r t SX| r t St S(   N(   Ru  Rv  R  Rw  R  Rx  Ri  R   R  R  R5   R   Rl  R   Ry  R]  RG  R  R  (   R  R  Rr  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4820  s    Oc            s   t  | |   } t t |  |   }   j d  t t t t | t t |  |     t | t	 | |  t
 d   t t t t
 d  | t
 d  |  t
 d  t
 d  t |  | | |   |   |  t |  |  |    |   S(   Ni  i   i   (   Ri  R   R  R  R  R
   R   R	   R  R2   R  R*   R   R  (   R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4820  s    c	   	         sQ     j  d  t t t | | | |  |  | | | |  |  |  |  S(   Ni  (   R  R   Rc  RG  (	   R8  R  Rp  R  R  R  R  t   qRk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4821  s    c            sg     j  d  t t t | | | |	  |  | | | |	  |
 | | | |	  |  |	  |	  S(   Ni  (   R  R   Rc  RG  (   R8  R=  R  t   rRp  R  R  R  t   HR  R  R;  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4822  s    c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4823  s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4823  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4824  s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t t d  t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4824  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4825  s    !(c            s   t  t | | | |  |  }   j d  t t d  | | t t t t d  | t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4825  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4826  s    !(c            s   t  t | | | |  |  }   j d  t t d  | | t t t t d  | t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   (   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4826  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4827  s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4827  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4828   s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4828  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4829  s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4829  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4830  s    !(c            s   t  t | | | |  |  }   j d  t | | | t t t | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R*   R   R  R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4830$  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4831*  s    !(c            s   t  t | | | |  |  }   j d  t | | t d  | | t t t | | | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement48312  s    !c         S   sp   t  | t t t t f  r t St t | | | |  |  } t t | | | |  | |  |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (   R  R  R  R  R  R  Rk  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With48328  s    !(c            s   t  t | | | |  |  }   j d  t | | t d  | | t t t | | | t d  | t d  t d  | t d  t d  d t | | | |  | |  |  |  | t | | | |  |  |  S(   Ni  i   i   i(   R   R  R  R  R  R*   R   R  (   R  R  R  R  R  R  Rk  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4832@  s    !c	   
      S   sp   t  | t t t t f  r t St t | | | |  |  }	 t t | | | |  |	 | |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (
   Rr  R  R  R  R  R  R  R  Rk  R;  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4833F  s    !(c	   
   	      s~   t  t | | | |  |  }	   j d  t | t t |  t | | | |  | |  |  t t | |   |  S(   Ni  (   R   R  R  R  R   RG  R  (
   Rr  R  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4833N  s    !c	   
      S   sp   t  | t t t t f  r t St t | | | |  |  }	 t t | | | |  |	 | |  rl t	 St S(   N(
   Ru  Rv  R  Rw  R  Rx  R   R  Rl  Ry  (
   Rr  R  R  R  R  R  R  R  Rk  R;  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4834T  s    !(c	   
   	      s~   t  t | | | |  |  }	   j d  t | t t |  t | | | |  | |  |  t t | |   |  S(   Ni  (   R   R  R  R  R   RG  R  (
   Rr  R  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4834\  s    !c         S   s   t  |  t t t t f  r t Syh t | |   } t t |  |   } t	 t
 t |   t t t |  |   | t |  |    } Wn t t f k
 r t SX| r t St S(   N(   Ru  Rv  R  Rw  R  Rx  Ri  R   R  R  R5   R   Rl  R   R  R  R  Ry  (   R  R  Rr  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4835b  s    Dc            s   t  | |   } t t |  |   }   j d  t t t t | t t |  |     t | t	 | |  t
 d   t t t t
 d  t |  | | t |  |   |   |  t |  |  |    |   S(   Ni  i   (   Ri  R   R  R  R  R
   R   R	   R  R2   R  R*   R   R  R  (   R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4835o  s    c         S   s   t  |  t t t t f  r t Syh t | |   } t t |  |   } t	 t
 t |   t t t |  |   | t |  |    } Wn t t f k
 r t SX| r t St S(   N(   Ru  Rv  R  Rw  R  Rx  Ri  R   R  R  R5   R   Rl  R   R  R  R  Ry  (   R  R  Rr  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4836v  s    Dc            s   t  | |   } t t |  |   }   j d  t t t t | t t |  |     t | t	 | |  t
 d   t t t t
 d  t |  | | t |  |   |   |  t |  |  |    |   S(   Ni  i   (   Ri  R   R  R  R  R
   R   R	   R  R2   R  R*   R   R  R  (   R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4836  s    c            s4     j  d  t | | |  t t |  |  |  S(   Ni  (   R  R  R   RG  (   R8  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4837  s    c            s4     j  d  t | | |  t t |  |  |  S(   Ni  (   R  R  R   RG  (   R8  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4838  s    c            s4     j  d  t | | |  t t |  |  |  S(   Ni  (   R  R  R   RG  (   R8  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4839  s    c         S   s|   t  | t t t t f  r t Sy4 t t |   t |  |  } t t	 |   } Wn t
 t f k
 rm t SX| rx t St S(   N(   Ru  Rv  R  Rw  R  Rx  R  RG  R5   R   R  R  Ry  (   t   yR  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4840  s    c            sQ   t  t |   t |  |  }   j d  t | t t t |   |   |  S(   Ni  (   R  RG  R  R  RO  R   (   R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4840  s    c         S   s   t  | t t t t f  r t Sy8 t t | |   t |  |  } t t	 |   } Wn t
 t f k
 rq t SX| r| t St S(   N(   Ru  Rv  R  Rw  R  Rx  R  RG  R5   R   R  R  Ry  (   R  t   wR  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4841  s    "c            sY   t  t | |   t |  |  }   j d  t | t t t | |   |   |  S(   Ni  (   R  RG  R  R  RO  R   (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4841  s    "c         S   s|   t  | t t t t f  r t Sy4 t t |   t |  |  } t t	 |   } Wn t
 t f k
 rm t SX| rx t St S(   N(   Ru  Rv  R  Rw  R  Rx  R  RG  R5   R   R  R  Ry  (   R  R  R  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4842  s    c            s^   t  t |   t |  |  }   j d  t | t |  | t d   | t d  |  S(   Ni  i   (   R  RG  R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4842  s    c         S   s   t  | t t t t f  r t SyE t t | |   t | |  | |  |  } t t	 |   } Wn t
 t f k
 r~ t SX| r t St S(   N(   Ru  Rv  R  Rw  R  Rx  R  RG  R5   R   R  R  Ry  (   t   zR  R  R  R  R  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4843  s    /c            s   t  t | |   t | |  | |  |  }   j d  t | t | | t d  |  | t d   | t d  |  S(   Ni  i   (   R  RG  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4843  s    /c   	         s   t  | | | |   }   j d  t | t |  | | |  t |  | t | |  |  t |  t | |  |  t |  t t  |  t | |  | |  |  |  S(   Ni  (   RG  R  R  R$   R%   R   R   (	   R8  R  R  R  R  R  R  Rk  Rr  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4844  s    c	   
         s   t  | | | |   }	   j d  t | t |  | | |	 |  t |  | |	 |  t |  t | |	 | |  t  |  |  |  S(   Ni  (   RG  R  R  R$   R%   R   (
   R8  R  R  R  R  R  R  R  Rk  Rr  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4845  s    c         S   s   t  |  t t t t f  r t Sy^ t | |   } t t |  |   } t	 t
 t |   t t t |  |   | |    } Wn t t f k
 r t SX| r t St S(   N(   Ru  Rv  R  Rw  R  Rx  Ri  R   R  R  R5   R   Rl  R   R  R  Ry  (   R  R  Rr  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4846  s    :c      	      s   t  | |   } t t |  |   }   j d  t | t | |  d  t t t d | d |  d d t |  | | |   |   |  t |  |  |   S(   Ni  i   i   (	   Ri  R   R  R  R  R2   R*   R   R  (   R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4846  s    c            sf     j  d  t | t | | |  | | |  t d  t | | |  | |  t |  |  S(   Ni  i   (   R  R   R  R  R  RG  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4847  s    c            sf     j  d  t | t | | |  | | |  t d  t | | |  | |  t |  |  S(   Ni  i   (   R  R   R  R  R  RG  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4848  s    c
   
   	      sa     j  d  t t | | | |	 | | |  |  | | |	 | | |  | |   |  S(   Ni  (   R  R   RG  (
   R8  R  R  R  R  R  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4849  s    c      	      s     j  d  t t | | | | | |
 |  |  |	 | | | |
 |  |  | | | | |
 |  | |   |  S(   Ni  (   R  R   RG  (   R8  R  R  R  R  R  R  R  R  R  R;  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4850  s    c      	      s|     j  d  t t | | |
 | |	 |  |  | | |
 | |	 |  |  | | |
 | |	 |  | |   |  S(   Ni  (   R  R   RG  (   R8  R  R  R  R  R  R  R  R  R;  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4851  s    c            sC     j  d  t | t | | | | |  | t |   |  S(   Ni  (   R  R   t   expRG  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4852  s    c            s      j  d  t t |  |   S(   Ni  (   R  R   R
  (   R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4853   s    c            sq   t  |  } t  |   }   j d  t | t |  | t |  | | t |  t | | | |  |  S(   Ni  (   RG  R  R  R$   R%   R   (   Rr  R8  R  R  R  t   uut   vv(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4854$  s    c            sk   t  |  } t  |   }   j d  t | | t |  | | t |  t | | | | |  |  S(   Ni  (   RG  R  R  R%   R   (   Rr  R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4855+  s    c   
         s   t  |  } t  |   } t  |  }	   j d  t | | t |  |	 | t |  | | |	 | t |  t | | | | |	 | | |  |  S(   Ni  (   RG  R  R  R%   R   (
   Rr  R  R8  R  R  R  R  R  R  t   ww(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With48562  s
    c         S   sB   t  |  t t t t f  r t St | |   } t |  r> t St S(   N(	   Ru  Rv  R  Rw  R  Rx  RH  R(   Ry  (   R  R  Rr  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4857:  s    c            s)   t  | |   }   j d  t | |   S(   Ni  (   RH  R  R   (   R  R  Rr  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4857B  s    c         S   sX  t  |  t t t t f  r t Syt t t t	 t  t t
 t   t t t d  |  t d  t t t | |   t d   |   t d  t d  t t | |   t d   t t t | |   t d   |   | |   |    } t | |   } t t | t d   |   } t | t  } Wn t t f k
 rIt SX| rTt St S(   Ni   i   (   Ru  Rv  R  Rw  R  Rx  R
   R   R	   t	   ShowStepst   StepCounterR  R   R  R  R   R  Ri  R   R  R  Ry  (   R  R  R  Rr  R  R  (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4858H  s    c            s  t  t t t t  t t t   t t t	 d  |  t	 d  t
 t t | |   t	 d   |   t	 d  t	 d  t t | |   t	 d   t
 t t | |   t	 d   |   | |   |    } t | |   } t
 t | t	 d   |   }   j d  t t d | t | |  d  t t t d | d |  d d t | d  | | |   |   |  t | d  |  |   |   S(   Ni   i   i  (   R
   R   R	   R  Rx  R  R  R   R  R  R   R  Ri  R  R  R  R2   R*   (   R  R  R  Rr  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4858V  s
    c            s&   t  |  }   j d  t | |   S(   Ni  (   RG  R  R   (   R  R  Rr  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4859^  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4860e  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4861j  s    c            sZ     j  d  t t | | | | t | | |  | t | | |  |  |  |  S(   Ni  (   R  R   Rc  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4862o  s    c            s     j  d  t | | | | t | | |  | t | | |  |  t d  |  t | | | | t | | |  | t d  t | | |  |  |  S(   Ni  i(   R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4863t  s    c            s     j  d  t | | | | t d  t | | |  |  t | | |  | t d  |  t | | | | t d  t | | |  |  t d  t | | |  | |  S(   Ni   i   i(   R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4864y  s    c      	      s     j  d  t | | | | t | | | | t d  t d  t | | |  | |  |  t | | | | t d  t | | |  | | | |  S(   Ni  ii   (   R  R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4865~  s    c      	      s     j  d  t | | | | t | | | | t d  t d  t | | |  | |  |  t | | | | t d  t | | |  | | | |  S(   Ni  ii   (   R  R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4866  s    c            s     j  d  t | |  | | t d  t | | | |  t d  t | | |  | t d  |  |  t | | | |  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4867  s    c      	      s     j  d  t | |  | | t d  t | | | |  t d  t d  t | | |  | t d  |  |  t | | | |  t d  t | | |  | t d  | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4868  s    c            s     j  d  t | | | | t | | |  |  t d  t | | |  t d  |  t | | | | t | | |  |  t d  t | | |  |  S(   Ni  ii   (   R  R   R  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4869  s    c            s     j  d  t | | | | t d  t | | |  | t | | |  |  t d  |  t | | | | t d  t | | |  | t d  t | | |  |  t d  |  S(   Ni  i   ii   (   R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4870  s    c            s     j  d  t | | | | t d  t | | |  |  t d  t | | |  t d  |  t | | | | t d  t | | |  |  t d  t | | |  |  S(   Ni  i   ii   (   R  R   R  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4871  s    c            s     j  d  t | | | | t d  t | | |  | t d  t | | |  |  t d  |  t | | | | t d  t | | |  | t d  t d  t | | |  |  t d  |  S(   Ni  i   ii   (   R  R   R  R  R  (   R8  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4872  s    c   	         s   t  t d  t | | |  | t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i	  i(   R  R  R  R  R  R  R   (	   R8  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4873  s    Ac   	         s   t  t d  t | | |  | t d  t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i
  i(   R  R  R  R  R  R  R   (	   R8  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4874  s    Kc      	      sp     j  d  t t d  | t | | | |  t d  t t d  | t d  | |  | |  |  S(   Ni  i   i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4875  s    c   	         s   t  t d  t | | |  | t d  t | | |  |  |  }   j d  t | | t | | | | | t d  |  |  t | | | | | |  S(   Ni   i  i(   R  R  R  R  R  R  R   (	   R8  R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4876  s    Kc	   	         sU     j  d  t t | |  | | t |  |   | | t |  |   | |  S(   Ni  (   R  R   R1  (	   Rr  R  R8  R  R  Rp  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4877  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4878  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4879  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4880  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4881  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4882  s    c	   	   	      s     j  d  t | |  | | | t d  t | | t | | |  | t d  | | | |  t d  |  |  t | | t | | |  | t d  | | | |  | | | t d  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4883  s    R  c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4884  s    c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4885  s    c
   
         sZ     j  d  t t |	 | | | t | | |  |  t | | |  | |  |  S(   Ni  (   R  R   Rc  R  R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4886  s    c            s]     j  d  t t |
 | | | | | | |  |	 | | | | |  | | |  |  S(   Ni  (   R  R   Rb  (   R8  R  R=  R  Rp  R  R  R  R  R  R;  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4887  s    c            s     j  d  t | | | |  | | t | | |  |  t d  | t d  t |  t d  | t d  |  t | | | |  | |  | t |  t | | |  |  t d  | t d  t |  t d  | t d  |  S(   Ni  i   (   R  R  R  R  RO  R  (   R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4888  s    c            s     j  d  t | | | |  | | t | | |  |  t d  | t d  t |  t d  | t d  |  t | | | |  | |  | t |  t | | |  |  t d  | t d  t |  t d  | t d  |  S(   Ni  i   (   R  R  R  R  RO  R  (   R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4889  s    c            s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | |  | t |  t | | |  | |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni  i   ii(   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4890  s    c            s    j  d  t | t d  |  |  t d  | t d  | t d  t |  t d  | t d  |  t d  t | | | | | t | | |  |  t d  |  |  t | | | | | | | t |  t | | |  |  | t d  | t d  t |  t d  | t d  |  t d  |  t | | | | | | |  t | | |  t | | |  |  t d  | t d  | t d  t |  t d  | t d  |  t d  |  S(   Ni  i   ii(   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4891  s    c            s     j  d  t | | | |  | t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R  R  RO  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4892  s    c            s     j  d  t | | | |  | t | | |  t | | |  | t d  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  R  R  RO  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4893  s    c            s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4894  s    c            s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t | | |  | t d  |  |  t | | | |  | t | | |  t | | |  | t d  | | t d  |  t | | | |  | |  | t |  t | | |  | t d  | t d  | t d  | t d  |  S(   Ni  i   i   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4895  s    c      	      s     j  d  t t t d  t | | |  t d  | t t | | | |  t | | |  | t | | | |  | t t d  t | | |  t d  | t t | | | |  |  |  S(   Ni   i   i(   R  R  R  R  R  R  R   (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4896  s    c      	      s     j  d  t t t d  t | | |  t d  | t t | | | |  t | | |  | t | | | |  | t t d  t | | |  t d  | t t | | | |  |  |  S(   Ni!  i   i   (   R  R  R  R  R  R  R   (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4897!  s    c      
      s     j  d  t t | t t | | | |  | t t d  t | | |  t d  | t t d  t | | |  t d  | |  |  |  S(   Ni"  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4898&  s    c      
      s     j  d  t t | t t | | | |  | t t d  t | | |  t d  | t t d  t | | |  t d  | |  |  |  S(   Ni#  i   i   (   R  R  R  R   R   R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4899+  s    c      	      s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | |  | t d  t | | |  | t |  |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t d  t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni$  i   i   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement49000  s    c      	      s    j  d  t | t d  | | t d  |  t d  | t d  t |  t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | |  | t d  t | | |  | t |  |  t d  | t d  t |  t d  | t d  | t d  |  t | | | |  | | | t d  t | | |  | t d  t | | |  |  t d  | t d  t |  t d  | t d  | t d  |  S(   Ni%  i   i   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement49015  s    c            s     j  d  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni&  i   iii   (   R  R  R  R  R  RO  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4902:  s    c            s     j  d  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni'  i   iii   (   R  R  R  R  R  RO  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4903?  s    c      	      s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni(  i   iii   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4904D  s    c      	      s    j  d  t |  t d  | t d  t |  t d  | t d  | t d  t d  | t d  | t d  | t d  t | | | |  | t d  t | | |  | t d  |  |  t | | | |  | t d  t | | |  | t d  t | | |  | | t d  |  t | | | |  | |  | t d  t | | |  | t d  t |  | t d  | t d  | t d  |  S(   Ni)  i   iii   (   R  R  R  RO  R   R  R  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4905I  s    c            s    j  d  t t d  | | | | |  | t | t |  | t |  t d  | | t d  t |  | t |  t d  | | t d  t d  t t d  t | | |   t t | | | |  |  | t |  t | | |  S(   Ni*  i   i   (   R  R  R  R4   R  RO  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4906N  s    c            s    j  d  t | | | |  | t d  t | t | t |  | t |  t d  | | t d  t |  | t |  t d  | | t d  t d  t t d  t | | |   t t | | | |  |  | t |  t | | |  S(   Ni+  i   i   (   R  R  R  R  R4   RO  R  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4907S  s    c      
      s     j  d  t t t d  t | | |  t d  | t d  t | | |  | t t | | | |  t t | | | |  | t t d  t | | |  t d  | t t | | | |  |  |  |  S(   Ni,  i   i   (   R  R  R  R  R  R  R   R,  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4908X  s    c            s     j  d  t t d  t t d  t | | |  | t d  t | | |  | t t | | | |  t t | | | |  | t d  t t d  t | | |  | t t | | | |  |  |  |  S(   Ni-  i   i   (   R  R  R  R  R  R  R   R,  (   R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4909]  s    c
   
   	      s     j  d  t t d  | | | t | | | | | t t | t d  |  | t d  |	 | t d   t d  | |  |  S(   Ni.  i   i   (   R  R  R  R   R  t   Pi(
   R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4910b  s    c
   
   	      s|     j  d  t t d  | | | t | | | | | t | t d  |	 | t d   t d  | |  |  S(   Ni/  i   (   R  R  R  R   R  (
   R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4911g  s    c
   
   	      s|     j  d  t t d  | | | t | | | | | t | t d  |	 | t d   t d  | |  |  S(   Ni0  i   (   R  R  R  R   R  (
   R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4912l  s    c      	      s|     j  d  t | | t |	 | | | | t t | t d  | | t d  |
 | t d   |  |  |  S(   Ni1  i   i   (   R  R  R   R  R  R  (   R  R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4913q  s    c      	      sd     j  d  t | | t |	 | | | | t | t d  |
 | t d   |  |  |  S(   Ni2  i   (   R  R  R   R  R  (   R  R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4914v  s    c      
      sn     j  d  t | | t |	 | | | | t d  t | t d  |
 | t d   |  |  |  S(   Ni3  i   i   (   R  R  R   R  R  (   R  R7  R  R=  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4915{  s    t   ic      
      s     j  d  t t d  | t |	 | | | | t | |
 |  | |  t | |
 |  |  |  t |	 | | | | | | t | |
 |  | |  t | |
 |  |  S(   Ni4  i   (   R  R  R  R   R  R  (   R7  R  R=  R  R  R  R  R  t   hRk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4916  s    c      
      s     j  d  t t d  | t |	 | | | | t | |
 |  | |  t | |
 |  |  |  t |	 | | | | | | t | |
 |  | |  t | |
 |  |  S(   Ni5  i   (   R  R  R  R   R  R  (   R7  R  R=  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4917  s    c            sB     j  d  t | | t | |  | t |  |   | |  S(   Ni6  (   R  R   R1  (   Rr  R  Rp  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4918  s    c	   
         s   t  | | | | | t | | |  | |  }	   j d  t |  t |	 | |  t d  |  |  t | |  |	 |  S(   Ni7  i(   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  Rk  R;  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4919  s    5c	   
         s   t  | | | | | t | | |  | |  }	   j d  t |  t |	 | |  t d  |  |  t | |  |	 |  S(   Ni8  i(   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  Rk  R;  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4920  s    5c            s^     j  d  t t |	 | | | | t | |
 |  |  t | | |  | |  |  S(   Ni9  (   R  R   Rc  R  R  (   R  R=  R7  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4921  s    c            sf     j  d  t t |
 | | | |	 |	 |  t | | |	  | t | | |	  | |	  |	  S(   Ni:  (   R  R   Rc  R  R  (   R8  R  R=  R7  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4922  s    c            s^     j  d  t t |	 | | | | | | |
 |  |  | | |
 |  | |  |  S(   Ni;  (   R  R   Rg  (   R  R  Rp  R  R  R  R  R  R  Rk  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4923  s    c            s4     j  d  t t | | t |   | |  |  S(   Ni<  (   R  R   Rg  R  (   Rr  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4924  s    c            s4     j  d  t t | | t |   | |  |  S(   Ni=  (   R  R   Rg  R  (   Rr  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4925  s    c            sB     j  d  t t | | t |   | t |   | |  |  S(   Ni>  (   R  R   Rg  R  R  (   Rr  R  R  R  R  Rk  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4926  s    c            s     j  d  t | |  t d  t | | t | | |   |  t d  |  t d  |  t | t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Ni?  i   i   (   R  R  R  R  RO  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4927  s    c      
      s     j  d  t | |  t d  t | | t | | |   |  t d  |  t d  |  t | t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Ni@  i   i   (   R  R  R  R  RO  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4928  s    c            s     j  d  t t | | | t d  | |  t | | | |   t d  | | |  | | | t d  | |  t | | | |   t d  | | |  |  |  |  S(   NiA  i   i   (   R  R   R   R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4929  s    c            s     j  d  t t | | | t d  | |  t | | | |   t d  | | | t d  | |  t | | | |   t d  |  |  |  S(   NiB  i   i   (   R  R   R   R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4930  s    c      
      s     j  d  t | t | |  t | | |   |  t d  | t d  t d  |  t |  | | t | |  t | | |   |  t d  | t d  t d  |  S(   NiC  i   i   (   R  R  R  RO  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4931  s    c      
      s     j  d  t | t | |  t | | |   |  t d  | t d  t d  |  t |  | | t | |  t | | |   |  t d  | t d  t d  |  S(   NiD  i   i   (   R  R  R  RO  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4932  s    c      
      s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   NiE  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4933  s    c      
      s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t | | t | | |   t | | t | | |   |  t d  | t d  | t d  |  t d  t d  |  S(   NiF  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4934  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   NiG  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4935  s    c      
      s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t | | t | | |   |  t d  |  |  t | t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   NiH  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4936  s    c      
      s    j  d  t | t d  | | | t d  t | t t d  t |  t d  |  t | | | t | t t |  t | | | t | t t |  |  t |  t t | | |  t d  t d  | | t d  t t | | |  t d  t d  | | | | | t d  t | t t d  t |   t | | |  t d  |  S(   NiI  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4937  s    c      
      sz    j  d  t | | | | t | t t |  | | | t | t t |  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  t d  t d  | | t d  t t | | |  t d  t d  | | | | | t d  t | t t d  t |   t | | |  t d  |  S(   NiJ  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4938  s    c            s     j  d  t | | t d  |  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   NiK  i   i   (   R  R  R  R  RO  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4939  s    c      
      s     j  d  t | | t d  |  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   NiL  i   i   (   R  R  R  R  RO  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4940  s    c            s    j  d  t t d  |  t t | | | | | | t d  | |  | t d  t | | | |  | t d   | | |  | | | | t d  | |  | t d  t | | | |  | t d   | | |  |  |  |  |  S(   NiM  i   i   (   R  R  R  R   R   R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4941  s    c            s     j  d  t t d  |  t t | | | | | | t d  | |  t | | | |  | t d   | | | | t d  | |  t | | | |  | t d   |  |  |  |  S(   NiN  i   i   (   R  R  R  R   R   R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4942  s    c      
      s    j  d  t | |  t d  |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  t | | | |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   NiO  i   i   (   R  R  R  R  RO  R  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4943	  s    c      
      s    j  d  t | |  t d  |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  t | | | |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   NiP  i   i   (   R  R  R  R  RO  R  (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4944  s    c            s
    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  | t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   NiQ  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4945  s    c            s
    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  | t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t | | t | | |   t | | t | | |   |  t d  | t d  | t d  |  t d  | t d  t d  |  S(   NiR  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4946  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  t | | t d  | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   NiS  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4947  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t | | t | | |   |  t d  |  |  t | | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  t | | t d  | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   NiT  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4948"  s    c      
      s    j  d  t | | t d  t d  | | | t d  t | t t d  t |  t d  |  t | | | t | t t |  t | | | t | t t |  |  t |  t t | | |  | t d  t d  | | t d  t t | | |  | t d  t d  | | | | | t d  t | t t d  t |   t | | |  | t d  |  S(   NiU  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4949'  s    c      
      s    j  d  t | | t d  | | | t | t t |  | | | t | t t |  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  | t d  t d  | | t d  t t | | |  | t d  t d  | | | | | t d  t | t t d  t |   t | | |  | t d  |  S(   NiV  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4950,  s    c            s     j  d  t t d  t | |  |  t | | | t d  | | | | t d  | t t d  | |  |  |  |  S(   NiW  i   i   (   R  R  R  R  R   (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement49511  s    c            s     j  d  t t d  |  | t | |  |  t | | | t d  | | | | t d  | t t d  | |  |  |  |  S(   NiX  i   i   (   R  R  R  R  R   (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement49526  s    c            s     j  d  t | |  t d  t d  t | | t | | |   |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   NiY  ii   i(   R  R  R  R  RO  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4953;  s    c            s     j  d  t | |  t d  t d  t | | t | | |   |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   NiZ  ii   i(   R  R  R  R  RO  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4954@  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Ni[  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4955E  s    c            s    j  d  t | t d  | t d  |  t d  t d  t d  | t d  | t d  |  t d  |  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  t | t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Ni\  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4956J  s    c            s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Ni]  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4957O  s    c            s    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  t d  t t d  t | | t | | |   |  t d  |  |  t | t d  t | | t | | |   |  | t d  | t d  |  t d  t d  |  t | | |  | t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  t d  |  S(   Ni^  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4958T  s    c      
      s    j  d  t | | | | t | t t |  | | | t d  t | t t d  t |  t d  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  t d  t d  | | t d  t t | | |  t d  t d  | | | | | t d  t | t t d  t |   t | | |  t d  |  S(   Ni_  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4959Y  s    c      
      s    j  d  t | t | | | t | t t |  | | | t d  t | t t d  t |  t d  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  t d  t d  | | t d  t t | | |  t d  t d  | | | | | t d  t | t t d  t |   t | | |  t d  |  S(   Ni`  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4960^  s    c      
      s     j  d  t t d  t | | | |  t d   t | |  | | | |  t d  | | | | t d  |  t d  | t t d  | | | |  t d   |  |  S(   Nia  i   i   (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4961c  s    c      
      s     j  d  t t d  | | t | | | |  t d   |  t d  t | |  | | | |  t d  | | | | t d  |  t d  | t t d  | | | |  t d   |  |  S(   Nib  i   i   (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4962h  s    c            s    j  d  t | | t d  |  t d  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  S(   Nic  i   ii(   R  R  R  R  RO  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4963m  s    c            s    j  d  t | | t d  |  t d  t d  t | | t | | |   |  t d  | t d  |  t d  |  t | | t d  t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  S(   Nid  i   ii(   R  R  R  R  RO  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4964r  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | | |  t d  |  t | | t d  | t d  t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Nie  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4965w  s    c            s    j  d  t | t d  | t d  |  t d  t d  | t d  t d  | t d  | t d  |  t d  |  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  t d  t | | t | | |   |  t d  | | |  t d  t | | t | | |   |  t | | t d  | t d  t d  t | | t | | |   |  t d  | t d  | t d  |  t d  |  t d  |  S(   Nif  i   ii   i(   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4966|  s    c            s(    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  | t d  t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   Nig  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4967  s    c            s(    j  d  t | t d  | t d  |  |  t d  | t d  | t d  |  t d  | t d  t d  t | | t d  t | | t | | |   |  t d  |  |  t | | t d  | t d  t d  t | | t | | |   |  | t d  | t d  |  t d  | t d  t d  |  t | | |  | | t d  t d  t | | t | | |   |  t d  t | | t | | |   | t d  | t d  |  t d  | t d  t d  |  S(   Nih  i   i   (   R  R  R  R   R  RO  R  R  (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4968  s    c      
      s    j  d  t | | t d  | | | t | t t |  | | | t d  t | t t d  t |  t d  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  | t d  t d  | | t d  t t | | |  | t d  t d  | | | | | t d  t | t t d  t |   t | | |  | t d  |  S(   Nii  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4969  s    c      
      s    j  d  t | | t d  t | | | t | t t |  | | | t d  t | t t d  t |  t d  |  t d  | | | t d  t | t t d  t |  t d  |  t |  t t | | |  | t d  t d  | | t d  t t | | |  | t d  t d  | | | | | t d  t | t t d  t |   t | | |  | t d  |  S(   Nij  i   i   (   R  R  R  R  R  R4   (   R8  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4970  s    c      	      s     j  d  t | t t | |   | t d  t | |  t | |   |  |   |   t t | |  t | |   |  | |   S(   Nik  i(   R  R  R   RO  R  R  R  R  (   R  R  R8  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4971  s    c      	      s     j  d  t | t t | |   | t d  t | |  t | |   |  |   |   t t | |  t | |   |  | |   S(   Nil  i(   R  R  R   RO  R  R  R  R  (   R  R  R8  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4972  s    c      
      s    j  d  t |  | t t | |  |  t d  t | | | t | |  |   |  |  t | t d  | | t | | t | | | t | |  |   |  |  t | | t d  t | | | t | |  |   | | |  S(   Nim  ii   (   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4973  s    c      
      s    j  d  t |  | t t | |  |  t d  t | | | t | |  |   |  |  t | t d  | | t | | t | | | t | |  |   |  |  t | | t d  t | | | t | |  |   | | |  S(   Nin  ii   (   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4974  s    c      	      s     j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t t | | | t | |  |   | | |  S(   Nio  i(   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4975  s    c      	      s     j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t t | | | t | |  |   | | |  S(   Nip  i(   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4976  s    c      
      s    j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t | | t d  | | t | | | t | | | t | |  |   |  |  t | | | t d  t | | | t | |  |   | | |  S(   Niq  ii   (   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4977  s    c      
      s    j  d  t |  | t | | t | |  |  t d  t | | | t | |  |   |  |  t | | t d  | | t | | | t | | | t | |  |   |  |  t | | | t d  t | | | t | |  |   | | |  S(   Nir  ii   (   R  R  R   RO  R  R  R  R  (   R8  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4978  s    c      	      sk     j  d  t t d  |  t t t | |  | | t d  |  | t d  | |  |  |  S(   Nis  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4979  s    c      	      sk     j  d  t t d  |  t t t | |  | | t d  |  | t d  | |  |  |  S(   Nit  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4980  s    c      
      s     j  d  t t d  | t t t |  | | | | | | |  | |  | | t d  |  | t d  | | |  |  S(   Niu  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4981  s    c      
      s     j  d  t t d  | t t t |  | | | | | | |  | |  | | t d  |  | t d  | | |  |  S(   Niv  i   i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4982  s    c            s   t  | |   }   j d  t t |  t | t d   t | t d   |  t | t d   t | t d    | |   S(   Niw  i   i   i   i   (   R   R  R   R  R  R  (   R  R  R  t   lst(   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4983  s    c            s   t  | |   }   j d  t t |  t | t d   t | t d   |  t | t d   t | t d    | |   S(   Nix  i   i   i   i   (   R   R  R   R  R  R  (   R  R  R  R[  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   With4984  s    c            s,     j  d  t | t |   | | |  S(   Niy  (   R  R   R  (   Rr  R  R8  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4985  s    c            s,     j  d  t | t |   | | |  S(   Niz  (   R  R   R  (   Rr  R  R8  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4986  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni{  (   R  R   Rc  R  (   Rr  R  R8  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4987  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni|  (   R  R   Rc  R  (   Rr  R  R8  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4988  s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni}  (   R  R   Rc  R  (   Rr  R  R8  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4989  s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni~  (   R  R   Rc  R  (   Rr  R  R8  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4990  s    c            sI     j  d  t t d  | t | t t d  |   | |  |  S(   Ni  i   (   R  R  R  R   R  (   Rr  R  R8  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4991  s    c            s;     j  d  t t t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R  R  (   Rr  R  R8  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4992   s    c            sB     j  d  t t | | t |   | t |  | |  |  S(   Ni  (   R  R   Rc  R  R  (   Rr  R  R8  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4993  s    c            sy     j  d  t t |  |  t t |  | t d  t |  |  |  t t |   t |  | t d  |  S(   Ni  i(   R  R  R  R   R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4994
  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t d  t |  | t d  t |   |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4995  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t d  t |  | t d  t |   |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4996  s    c            sz     j  d  t t |  |  t t |  | t d  t |  |  |  t t |   t |  | t d  |  S(   Ni  i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4997  s    c            s     j  d  t t |  |  t t d  t |  | t d  |  |  t t |  |  t t d  t |  | t d  t |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4998  s    c            s     j  d  t t |  |  t t d  t |  | t d  |  |  t t |  |  t t d  t |  | t d  t |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement4999#  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t |  |  t t d  t |  | t d  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5000(  s    c            s     j  d  t t |  |  t t d  t |  | t d  t |  |  |  t t |  |  t t d  t |  | t d  |  |  S(   Ni  i   i(   R  R  R  R   R  R  R  (   Rr  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5001-  s    c	   	         sb     j  d  t | | t t d  | t d  | |  t d  | | | | |  |  S(   Ni  i   (   R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement50022  s    c      
      su     j  d  t t d  | t | |  t d  | | t t d  | t d  | |  | | |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement50037  s    c      
      su     j  d  t t d  | t | |  t d  | | t t d  | t d  | |  | | |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5004<  s    c
   
   
      s|     j  d  t | | t d  t t | | | |	 | | | t | | | |  |  |  | | | |  |  S(   Ni  i(   R  R  R  R*   R   R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5005A  s    c
   
   
      s|     j  d  t | | t d  t t | | | |	 | | | t | | | |  |  |  | | | |  |  S(   Ni  i(   R  R  R  R*   R   R  (
   R8  R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5006F  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R=  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5007K  s    c      
      sn     j  d  t t d  t | | | |  | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R=  R7  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5008P  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R=  R7  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5009U  s    c      
      sn     j  d  t t d  t | | | |  | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (   R  R=  R  R7  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5010Z  s    c	   	   
      s|     j  d  t t d  t | | | |  t d  | | | | | t t d  | t d  | |  |  |  S(   Ni  i   (   R  R  R  R   R  (	   R  R=  R  R7  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5011_  s    c      
      sB    j  d  t | | | |  t t | | |  | t | t t | | |  t | t d  | t d  t d   |  t | | | |  t t | | |  | t | t t | | |  t | t d  | t d  t d   |  t t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R   R  R  R  R  R  (   R  R=  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5012d  s    c            sS    j  d  t t t | | | |  t t | | |  | | t t | | |  t | t d  | t d  t d   |  |  t t t | | | |  t t | | |  | | t t | | |  t | t d  | t d  t d   |  |  t t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R=  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5013i  s    c            s\    j  d  t t t | | | |  t t | | |  t | | t t | | |  t | t d  | t d  t d   |  |  t t t | | | |  t t | | |  t | | t t | | |  t | t d  | t d  t d   |  |  t t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R  R  R   R  R  R  R  (   R  R=  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5014n  s    c      
      sL    j  d  t | | | |  t t | | |  t | t | t t | | |  t | t d  | t d  t d   |  t | | | |  t t | | |  t | t | t t | | |  t | t d  | t d  t d   |  t t | | | |  t d  | | |  t d  |  S(   Ni  i   i   (   R  R   R  R  R  R  R  (   R  R=  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5015s  s    c	   	   	      s     j  d  t t d  | t | | | |  t | | |  | t d  |  |  t t d  | t | | | |  t | | |  t | | |  | t d  |  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5016x  s    c	   	   	      s     j  d  t t d  | t | | | |  t | | |  | t d  |  |  t t d  | t | | | |  t | | |  | t d  t | | |  |  |  S(   Ni  i   i(   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5017}  s    c	   	         sG    j  d  t t d  | t | | | |  t | | |  t | | |  | t d  |  |  t | | t d  t | | | |  t | | |  | t d  |  |  t | t d  | t d  | t d  t | | | |  t | | |  | t d  | | t | | |  |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5018  s    c	   	         sG    j  d  t t d  | t | | | |  t | | |  | t d  t | | |  |  |  t | | t d  t | | | |  t | | |  | t d  |  |  t | t d  | t d  | t d  t | | | |  t | | |  | t d  | | t | | |  |  |  S(   Ni  i   ii   (   R  R  R  R   R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5019  s    c	   	   
      s     j  d  t |  | | | t t | | |  | | t | | |  |  |  t |  | | | t | | |  | | | | t | | |  |  S(   Ni  (   R  R  R   R  R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5020  s    c	   	   
      s     j  d  t |  | | | t t | | |  | | t | | |  |  |  t |  | | | t | | |  | | | | t | | |  |  S(   Ni  (   R  R  R   R  R  R  (	   R  R=  R  R  R  R  R  R  R;  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5021  s    c            s6     j  d  t | t |   | t |   | |  S(   Ni  (   R  R   R  R  (   Rr  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5022  s    c            s6     j  d  t | t |   | t |   | |  S(   Ni  (   R  R   R  R  (   Rr  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5023  s    c            sN     j  d  t t |  t | | |  | t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5024  s    c            sN     j  d  t t |  t | | |  | t | | |  | |  |  S(   Ni  (   R  R   Rc  R  (   R  R  R  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5025  s    c            s     j  d  t t d  t | | |  | |   t t | | |  |  |  t t d  t | | |  | |  t t | |  |  |  |  S(   Ni  i   (   R  R  R  R  R   R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5026  s    c      	      s     j  d  t t d  t | | |  | |   t t d  t | |  |  |  |  t t d  t | | |  | |  t t d  t | | |  |  |  S(   Ni  i   (   R  R  R  R  R   R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5027  s    c      	      s     j  d  t |  t | | |  | |  | t t d  t | |  |  t | | |  |  |  t |  | | |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5028  s    c      	      s|     j  d  t t | | |  | |  t t d  t | |  |  t | | |  |  |  t |  | | |  S(   Ni  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5029  s    c            s5     j  d  t | | t | |  |  | |  S(   Ni  (   R  R   R  (   Rr  R  R  R  R  R  (   R  (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   replacement5030  s    (   t    sympy.integrals.rubi.constraintsR*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R  t   u_R  R  R  t   x_R  R   R  t   A_t   n1_t   n2_t   p_t   m_R  t   n_t   F_t   a_t   G_R   t   H_t   v_t   y_t   w_t   z_t   f_t   h_RO  t   c_t   b_(  R  R*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   pattern4685R  t   rule4685t   pattern4686R  t   rule4686t   pattern4687R  t   rule4687t   pattern4688R  t   rule4688t   pattern4689R  t   rule4689t   pattern4690R  t   rule4690t   pattern4691R  t   rule4691t   pattern4692R  t   rule4692t   pattern4693R  t   rule4693t   pattern4694R  t   rule4694t   pattern4695R  t   rule4695t   pattern4696R  t   rule4696t   pattern4697R  t   rule4697t   pattern4698R  t   rule4698t   pattern4699R  t   rule4699t   pattern4700R  t   rule4700t   pattern4701R   t   rule4701t   pattern4702R  t   rule4702t   pattern4703R  t   rule4703t   pattern4704R  t   rule4704t   pattern4705R  t   rule4705t   pattern4706R  t   rule4706t   pattern4707R  t   rule4707t   pattern4708R  t   rule4708t   pattern4709R  t   rule4709t   pattern4710R	  t   rule4710t   pattern4711R
  t   rule4711t   pattern4712R  t   rule4712t   pattern4713R  t   rule4713t   pattern4714R  t   rule4714t   pattern4715R  t   rule4715t   pattern4716R  t   rule4716t   pattern4717R  t   rule4717t   pattern4718R  t   rule4718t   pattern4719R  t   rule4719t   pattern4720R  t   rule4720t   pattern4721R  t   rule4721t   pattern4722R  t   rule4722t   pattern4723R  t   rule4723t   pattern4724R  t   rule4724t   pattern4725R  t   rule4725t   pattern4726R  t   rule4726t   pattern4727R  t   rule4727t   pattern4728R  t   rule4728t   pattern4729R  t   rule4729t   pattern4730R  t   rule4730t   pattern4731R  t   rule4731t   pattern4732R  t   rule4732t   pattern4733R   t   rule4733t   pattern4734R!  t   rule4734t   pattern4735R"  t   rule4735t   pattern4736R#  t   rule4736t   pattern4737R$  t   rule4737t   pattern4738R%  t   rule4738t   pattern4739R&  t   rule4739t   pattern4740R'  t   rule4740t   pattern4741R(  t   rule4741t   pattern4742R)  t   rule4742t   pattern4743R*  t   rule4743t   pattern4744R+  t   rule4744t   pattern4745R,  t   rule4745t   pattern4746R-  t   rule4746t   pattern4747R.  t   rule4747t   pattern4748R/  t   rule4748t   pattern4749R0  t   rule4749t   pattern4750R1  t   rule4750t   pattern4751R2  t   rule4751t   pattern4752R3  t   rule4752t   pattern4753R4  t   rule4753t   pattern4754R5  t   rule4754t   pattern4755R6  t   rule4755t   pattern4756R9  t   rule4756t   pattern4757R:  t   rule4757t   pattern4758R<  t   rule4758t   pattern4759R>  t   rule4759t   pattern4760R?  t   rule4760t   pattern4761R@  t   rule4761t   pattern4762RA  t   rule4762t   pattern4763RB  t   rule4763t   pattern4764RC  t   rule4764t   pattern4765RD  t   rule4765t   pattern4766RE  t   rule4766t   pattern4767RF  t   rule4767t   pattern4768RG  t   rule4768t   pattern4769RH  t   rule4769t   pattern4770RI  t   rule4770t   pattern4771RJ  t   rule4771t   pattern4772RK  t   rule4772t   pattern4773RL  t   rule4773t   pattern4774RM  t   rule4774t   pattern4775RN  t   rule4775t   pattern4776RP  t   rule4776t   pattern4777RQ  t   rule4777t   pattern4778RR  t   rule4778t   pattern4779RS  t   rule4779t   pattern4780RT  t   rule4780t   pattern4781RU  t   rule4781t   pattern4782RV  t   rule4782t   pattern4783RW  t   rule4783t   pattern4784RX  t   rule4784t   pattern4785RY  t   rule4785t   pattern4786RZ  t   rule4786t   pattern4787R[  t   rule4787t   pattern4788R\  t   rule4788t   pattern4789R]  t   rule4789t   pattern4790R^  t   rule4790t   pattern4791R_  t   rule4791t   pattern4792R`  t   rule4792t   pattern4793Ra  t   rule4793t   pattern4794Rb  t   rule4794t   pattern4795Rc  t   rule4795t   pattern4796Rd  t   rule4796t   pattern4797Re  t   rule4797t   pattern4798Rf  t   rule4798t   pattern4799Rg  t   rule4799t   pattern4800Rh  t   rule4800t   pattern4801Ri  t   rule4801t   pattern4802Rj  t   rule4802t   pattern4803Rl  t   rule4803t   pattern4804Rn  t   rule4804t   pattern4805Ro  t   rule4805t   pattern4806Rq  t   rule4806Rs  t   pattern4807t   rule4807Rt  t   pattern4808t   rule4808Rz  t   pattern4809R{  t   rule4809R|  t   pattern4810R}  t   rule4810R~  t   pattern4811R  t   rule4811R  t   pattern4812R  t   rule4812R  t   pattern4813R  t   rule4813R  t   pattern4814R  t   rule4814R  t   pattern4815R  t   rule4815R  t   pattern4816R  t   rule4816R  t   pattern4817R  t   rule4817R  t   pattern4818R  t   rule4818R  t   pattern4819R  t   rule4819R  t   pattern4820R  t   rule4820t   pattern4821R  t   rule4821t   pattern4822R  t   rule4822R  t   pattern4823R  t   rule4823R  t   pattern4824R  t   rule4824R  t   pattern4825R  t   rule4825R  t   pattern4826R  t   rule4826R  t   pattern4827R  t   rule4827R  t   pattern4828R  t   rule4828R  t   pattern4829R  t   rule4829R  t   pattern4830R  t   rule4830R  t   pattern4831R  t   rule4831R  t   pattern4832R  t   rule4832R  t   pattern4833R  t   rule4833R  t   pattern4834R  t   rule4834R  t   pattern4835R  t   rule4835R  t   pattern4836R  t   rule4836t   pattern4837R  t   rule4837t   pattern4838R  t   rule4838t   pattern4839R  t   rule4839R  t   pattern4840R  t   rule4840R  t   pattern4841R  t   rule4841R  t   pattern4842R  t   rule4842R  t   pattern4843R  t   rule4843R  t   pattern4844t   rule4844R  t   pattern4845t   rule4845R  t   pattern4846R  t   rule4846t   pattern4847R  t   rule4847t   pattern4848R  t   rule4848t   pattern4849R  t   rule4849t   pattern4850R  t   rule4850t   pattern4851R  t   rule4851t   pattern4852R  t   rule4852t   pattern4853R  t   rule4853R  t   pattern4854t   rule4854R  t   pattern4855t   rule4855R  t   pattern4856t   rule4856R  t   pattern4857R  t   rule4857R  t   pattern4858R  t   rule4858R  t   pattern4859t   rule4859t   pattern4860R  t   rule4860t   pattern4861R  t   rule4861t   pattern4862R  t   rule4862t   pattern4863R  t   rule4863t   pattern4864R  t   rule4864t   pattern4865R  t   rule4865t   pattern4866R  t   rule4866t   pattern4867R  t   rule4867t   pattern4868R  t   rule4868t   pattern4869R  t   rule4869t   pattern4870R  t   rule4870t   pattern4871R  t   rule4871t   pattern4872R  t   rule4872R  t   pattern4873t   rule4873R  t   pattern4874t   rule4874t   pattern4875R  t   rule4875R  t   pattern4876t   rule4876t   pattern4877R  t   rule4877t   pattern4878R  t   rule4878t   pattern4879R  t   rule4879t   pattern4880R  t   rule4880t   pattern4881R  t   rule4881t   pattern4882R  t   rule4882t   pattern4883R  t   rule4883t   pattern4884R  t   rule4884t   pattern4885R  t   rule4885t   pattern4886R  t   rule4886t   pattern4887R  t   rule4887t   pattern4888R  t   rule4888t   pattern4889R  t   rule4889t   pattern4890R  t   rule4890t   pattern4891R  t   rule4891t   pattern4892R  t   rule4892t   pattern4893R  t   rule4893t   pattern4894R  t   rule4894t   pattern4895R   t   rule4895t   pattern4896R  t   rule4896t   pattern4897R  t   rule4897t   pattern4898R  t   rule4898t   pattern4899R  t   rule4899t   pattern4900R  t   rule4900t   pattern4901R  t   rule4901t   pattern4902R  t   rule4902t   pattern4903R  t   rule4903t   pattern4904R	  t   rule4904t   pattern4905R
  t   rule4905t   pattern4906R  t   rule4906t   pattern4907R  t   rule4907t   pattern4908R  t   rule4908t   pattern4909R  t   rule4909t   pattern4910R  t   rule4910t   pattern4911R  t   rule4911t   pattern4912R  t   rule4912t   pattern4913R  t   rule4913t   pattern4914R  t   rule4914t   pattern4915R  t   rule4915t   pattern4916R  t   rule4916t   pattern4917R  t   rule4917t   pattern4918R  t   rule4918R  t   pattern4919t   rule4919R  t   pattern4920t   rule4920t   pattern4921R  t   rule4921t   pattern4922R  t   rule4922t   pattern4923R  t   rule4923t   pattern4924R   t   rule4924t   pattern4925R!  t   rule4925t   pattern4926R"  t   rule4926t   pattern4927R#  t   rule4927t   pattern4928R$  t   rule4928t   pattern4929R%  t   rule4929t   pattern4930R&  t   rule4930t   pattern4931R'  t   rule4931t   pattern4932R(  t   rule4932t   pattern4933R)  t   rule4933t   pattern4934R*  t   rule4934t   pattern4935R+  t   rule4935t   pattern4936R,  t   rule4936t   pattern4937R-  t   rule4937t   pattern4938R.  t   rule4938t   pattern4939R/  t   rule4939t   pattern4940R0  t   rule4940t   pattern4941R1  t   rule4941t   pattern4942R2  t   rule4942t   pattern4943R3  t   rule4943t   pattern4944R4  t   rule4944t   pattern4945R5  t   rule4945t   pattern4946R6  t   rule4946t   pattern4947R7  t   rule4947t   pattern4948R8  t   rule4948t   pattern4949R9  t   rule4949t   pattern4950R:  t   rule4950t   pattern4951R;  t   rule4951t   pattern4952R<  t   rule4952t   pattern4953R=  t   rule4953t   pattern4954R>  t   rule4954t   pattern4955R?  t   rule4955t   pattern4956R@  t   rule4956t   pattern4957RA  t   rule4957t   pattern4958RB  t   rule4958t   pattern4959RC  t   rule4959t   pattern4960RD  t   rule4960t   pattern4961RE  t   rule4961t   pattern4962RF  t   rule4962t   pattern4963RG  t   rule4963t   pattern4964RH  t   rule4964t   pattern4965RI  t   rule4965t   pattern4966RJ  t   rule4966t   pattern4967RK  t   rule4967t   pattern4968RL  t   rule4968t   pattern4969RM  t   rule4969t   pattern4970RN  t   rule4970t   pattern4971RO  t   rule4971t   pattern4972RP  t   rule4972t   pattern4973RQ  t   rule4973t   pattern4974RR  t   rule4974t   pattern4975RS  t   rule4975t   pattern4976RT  t   rule4976t   pattern4977RU  t   rule4977t   pattern4978RV  t   rule4978t   pattern4979RW  t   rule4979t   pattern4980RX  t   rule4980t   pattern4981RY  t   rule4981t   pattern4982RZ  t   rule4982R\  t   pattern4983t   rule4983R]  t   pattern4984t   rule4984t   pattern4985R^  t   rule4985t   pattern4986R_  t   rule4986t   pattern4987R`  t   rule4987t   pattern4988Ra  t   rule4988t   pattern4989Rb  t   rule4989t   pattern4990Rc  t   rule4990t   pattern4991Rd  t   rule4991t   pattern4992Re  t   rule4992t   pattern4993Rf  t   rule4993t   pattern4994Rg  t   rule4994t   pattern4995Rh  t   rule4995t   pattern4996Ri  t   rule4996t   pattern4997Rj  t   rule4997t   pattern4998Rk  t   rule4998t   pattern4999Rl  t   rule4999t   pattern5000Rm  t   rule5000t   pattern5001Rn  t   rule5001t   pattern5002Ro  t   rule5002t   pattern5003Rp  t   rule5003t   pattern5004Rq  t   rule5004t   pattern5005Rr  t   rule5005t   pattern5006Rs  t   rule5006t   pattern5007Rt  t   rule5007t   pattern5008Ru  t   rule5008t   pattern5009Rv  t   rule5009t   pattern5010Rw  t   rule5010t   pattern5011Rx  t   rule5011t   pattern5012Ry  t   rule5012t   pattern5013Rz  t   rule5013t   pattern5014R{  t   rule5014t   pattern5015R|  t   rule5015t   pattern5016R}  t   rule5016t   pattern5017R~  t   rule5017t   pattern5018R  t   rule5018t   pattern5019R  t   rule5019t   pattern5020R  t   rule5020t   pattern5021R  t   rule5021t   pattern5022R  t   rule5022t   pattern5023R  t   rule5023t   pattern5024R  t   rule5024t   pattern5025R  t   rule5025t   pattern5026R  t   rule5026t   pattern5027R  t   rule5027t   pattern5028R  t   rule5028t   pattern5029R  t   rule5029t   pattern5030R  t   rule5030(    (   R  sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   miscellaneous_trig   s       d}}}}kk 6 6uu  }}kk 6 6uu  0}}}}kk 6 6uu 0 0 " /  2   , ,   & & & & ) ) ) ) ,ouun	k	k	k	k	n	w	n	w	n	n			k	k	k	k	q	q	q	q	q	q					%	)	>	X	! <<e	!	$   P $ $     F BB_||ss44aaQQhhdQhAKKAKKKK  T T{{~~t~}N(d  t   __doc__t   sympy.externalR    R   t   sympy.utilities.decoratorR   R   R   R   R   t%   sympy.integrals.rubi.utility_functionR   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R!  R"  R#  R$  R%  R&  R'  R(  R)  R*  R+  R,  R-  R.  R/  R0  R1  R2  R3  R4  R5  R6  R7  R8  R9  R:  R;  R<  R=  R>  R?  R@  RA  RB  RC  RD  RE  RF  RG  RH  RI  RJ  RK  RL  RM  RN  RO  RP  RQ  RR  RS  RT  RU  RV  RW  RX  RY  RZ  R[  R\  R]  R^  R_  R`  Ra  Rb  Rc  Rd  Re  Rf  Rg  Rh  Ri  Rj  Rk  Rl  Rm  Rn  Ro  Rp  Rq  Rr  Rs  Rt  Ru  Rv  Rw  Rx  Ry  Rz  R{  R|  R}  R~  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  RO  R  R  R  t   sympyR  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   sympy.integrals.rubi.symbolR  t   sympy.core.symbolR  R  t   sympy.functionsR  R  R  R  R  R  R  t%   sympy.functions.elementary.hyperbolicR  R  R  R  R  R  R  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  R  R  R  t   B_t   C_R  R  R  R  R  R  t   d_t   e_R  t   g_R  t   i_t   j_t   k_t   l_R  R  R  t   q_t   r_t   t_R  R  t   s_R  R  R  R  t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_R  R  t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_t   Px_t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   RR  R  Rm  R  Rx  t	   _UseGammaR  t   NoneR  RU  (    (    (    sL   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_trig.pyt   <module>   s>   "           1nj:R4|'	