
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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   J  D      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 tV tW tX tY tZ d t[ d   tZ d t[ d   t\ tZ d t[ d   t] tY  | | | | | | |  }V   f d   }W t^ |V |W  }X tV tW t_ tY tZ d t[ d   tZ d t[ d   t] tZ d t[ d   t` tZ d	 t[ d   tY  | | | |	 | |
 | | 	 }Y   f d
   }Z t^ |Y |Z  }[ tV tW tY tZ d t[ d   tZ d t[ d   t\ tZ d t[ d   t] tZ d t[ d   t` tZ d	 t[ d   tY  | | | |	 | | |
 | | 
 }\   f d   }] t^ |\ |]  }^ tV tW ta tb tY tZ d t[ d   tZ d t[ d    tZ d t[ d   tZ d t[ d   tb tY tZ d t[ d   tZ d t[ d    tZ d t[ d   tZ d t[ d   tY t[ d  tZ d t[ d   tY tZ d t[ d   tZ d t[ d   tY  | | | |	 | | | | | | | | | | |  }_   f d   }` t^ |_ |`  }a tV tW ta tb tY tZ d t[ d   t[ d   tZ d t[ d   tZ d t[ d   tb tY tZ d t[ d   t[ d   tZ d t[ d   tZ d t[ d   tY t[ d  tZ d t[ d   tZ d t[ d   tY  | | | | | | | | | |  }b   f d   }c t^ |b |c  }d tV tW ta tb tY tZ d t[ d   tZ d t[ d    tZ d t[ d   tb tY tZ d t[ d   tZ d t[ d    tZ d t[ d   tZ d t[ d   tZ d t[ d   tY t[ d  tZ d t[ d   tY tZ d t[ d   tZ d t[ d   tY  | | | |	 | | | | | | | | | | |  }e   f d   }f t^ |e |f  }g tV tW ta tb tY tZ d t[ d   t[ d   tZ d t[ d   tb tY tZ d t[ d   t[ d   tZ d t[ d   tZ d t[ d   tZ d t[ d   tY t[ d  tZ d t[ d   tZ d t[ d   tY  | | | | | | | | | |  }h   f d   }i t^ |h |i  }j d   }k tV tW tX tc tY  td |k   }l   f d   }m t^ |l |m  }n d   }o tV tW tX te tc tY  td |o   }p   f d   }q t^ |p |q  }r d   }s tV tW tX tc tZ d t[ d   tY  | | td |s   }t   f d   }u t^ |t |u  }v d    }w tV tW tX tc tZ d t[ d   tf tZ d t[ d   tY  | | | td |w   }x   f d!   }y t^ |x |y  }z d"   }{ tV tW tX tY  td |{   }|   f d#   }} t^ || |}  }~ tV tW tb tY tZ d t[ d   tZ d t[ d   tZ d t[ d    tZ d t[ d   tb tY tZ d t[ d   tZ d t[ d   tZ d t[ d    tZ d t[ d   tg tZ d	 t[ d   tY  | | | |	 | | | | | 
 }   f d$   } t^ | |  } tV tW tb tY tZ d t[ d   tZ d t[ d   tZ d t[ d    tZ d t[ d   tb tY tZ d t[ d   tZ d t[ d   tZ d t[ d    tZ d t[ d   tg tZ d	 t[ d   tY  | | | |	 | | | | | 
 }   f d%   } t^ | |  } tV tW tX tZ d t[ d   te tX t\ tZ d t[ d   th tZ d& t[ d   tY  | | | | | |  }   f d'   } t^ | |  } d(   } tV tW tX th tZ d t[ d   tZ d t[ d   tZ d t[ d   tc tZ d t[ d   tZ d t[ d   tZ d t[ d   tY  | | | |	 | | | td |  	 }   f d)   } t^ | |  } d*   } tV tW tX th tZ d t[ d   tZ d t[ d   tZ d t[ d   te tZ d t[ d   tZ d t[ d   tZ d& t[ d   tc tZ d t[ d   tZ d t[ d   tZ d t[ d   tY  | | | |	 | | | | | | |  td |   }   f d+   } t^ | |  } d,   } tV tW tX th tZ d t[ d   tZ d t[ d   tZ d t[ d   te tZ d t[ d   tZ d t[ d   tZ d& t[ d   tc tZ d t[ d   tZ d t[ d   tZ d t[ d   tf tZ d- t[ d   tZ d t[ d   tZ d. t[ d   tY  | | | |	 | | | |" | | | |
 | |  |! td |   }   f d/   } t^ | |  } d0   } tV tW ti tc t\ tZ d t[ d   tZ d	 t[ d   tY  | | | |# td |   }   f d1   } t^ | |  } d2   } tV tW tc t\ tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | |$ td |   }   f d3   } t^ | |  } d4   } tV tW th tZ d t[ d   tc t\ tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | |% td |   }   f d5   } t^ | |  } d6   } tV tW th tZ d7 t[ d   tZ d t[ d   tc t\ tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | | |& | td |  	 }   f d8   } t^ | |  } d9   } tV tW tj tc t\ tZ d t[ d   th t\ tZ d t[ d   te tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | | | |& | |  td |   }   f d:   } t^ | |  } d;   } tV tW tj tc t\ tZ d t[ d   te tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | | |& |  td |  
 }   f d<   } t^ | |  } d=   } tV tW th tZ d t[ d   te tZ d7 t[ d   tZ d t[ d   tc t\ tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | | |& |  td |  
 }   f d>   } t^ | |  } d?   } tV tW tf tZ d t[ d   tj tc t\ tZ d t[ d   th t\ tZ d t[ d   te tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | | | | |& | |  td |   }   f d@   } t^ | |  } dA   } tV tW tf tZ d t[ d   tj tc t\ tZ d t[ d   te tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tZ d	 t[ d   tY  | | | | | | | |& |  td |   }   f dB   } t^ | |  } dC   } tV tW th t\ tZ d t[ d   tZ d t[ d   tZ d& t[ d   tc t\ tZ d t[ d   tZ d t[ d   tZ d t[ d   tZ d	 t[ d   tY  | | | |	 | | | | td |  
 }   f dD   } t^ | |  } dE   } tV tW th t\ tZ d t[ d   tZ d t[ d   tZ d& t[ d   te t\ tZ d t[ d   tZ d t[ d   tZ d. t[ d   tc t\ tZ d t[ d   tZ d t[ d   tZ d t[ d   tZ d	 t[ d   tY  | | | |	 | | | | | |
 | |  td |   }   f dF   } t^ | |  } dG   } tV tW ta th tX tY  | | td |   }   f dH   } t^ | |  } dI   } tV tW ta th tX te tZ d t[ d   tY  | | |' td |   }   f dJ   } t^ | |  } dK   } tV tW tX ti th tZ d& t[ d   te tZ d& t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | | td |   }   f dL   } t^ | |  } dM   } tV tW tX th tZ dN t[ d   ti th tZ d& t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |+ |( |) |* td |   }   f dO   } t^ | |  } dP   } tV tW tX th tZ dN t[ d   te tZ dQ t[ d   ti th tZ d& t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |+ |- |, |) |* td |   }   f dR   } t^ | |  } dS   } tV tW tX th tZ d& t[ d   tZ d t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |. | |/ td |  
 }   f dT   } t^ | |  } dU   } tV tW tX th tZ dN t[ d   th tZ d& t[ d   tZ d t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |+ |0 |1 |/ td |   }   f dV   } t^ | |  } dW   } tV tW tX te tZ dQ t[ d   th tZ d& t[ d   tZ d t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |- |2 |3 |4 |/ td |   }   f dX   } t^ | |  } dY   } tV tW tX th tZ dN t[ d   te tZ dQ t[ d   th tZ d& t[ d   tZ d t[ d   te tZ d. t[ d   tZ d t[ d   tZ d t[ d   tY  | | | | |
 |+ |- |5 |3 |4 |/ td |   }   f dZ   } t^ | |  } tV tW tX tY tZ d t[ d   tY  | | |6  }   f d[   } t^ | |  } d\   } tV tW tX tY  td |   }   f d]   } t^ | |  } d^   } tV tW tX tY  td |   }   f d_   } t^ | |  } tV tW th tZ d t[ d   te tZ d t[ d   tf tZ d. t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | |
 | | |7 |8 
 }   f d`   } t^ | |  } tV tW th tZ d t[ d   te tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | | | |7  }   f da   } t^ | |  } tV tW th tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | | |9 |:  }   f db   } t^ | |  } tV tW tY t\ tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | |; |< |=  }   f dc   } t^ | |  } tV tW th t\ tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | |< |> |?  }   f dd   } t^ | |  } tV tW th t\ tY tZ d t[ d   tZ d t[ d   tZ d t[ d   t] tZ d	 t[ d   tY  | | | | | |< |>  }   f de   } t^ | |  } df   }tV tW tY tZ dN t[ d   tZ d t[ d   tY tZ dQ t[ d   tZ d t[ d   tg tZ d	 t[ d   tY  | | | |+ |- |@ |A td | 	 }  f dg   }t^ || }dh   }tV tW tX ti tY t\ tZ d t[ d   tY  | | |B td |  }  f di   }t^ || }tV tW tX tY tZ d t[ d   tZ d t[ d   tY tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tY  | | | | |& |C | |D 	 }	  f dj   }
t^ |	|
 }tV tW tX tY tZ d t[ d   tZ d t[ d   tY tZ d7 t[ d   tZ d t[ d   tZ d t[ d   t] tY  | | | | | |& |C | |D 
 }  f dk   }t^ || }dl   }tV tW tX tY tZ d t[ d   tZ d t[ d   tY tZ d7 t[ d   tZ d t[ d   tZ d t[ d   tY  | | | |& |B td |  }  f dm   }t^ || }tV tW tZ d	 t[ d   tY tZ d t[ d   tZ d t[ d   tb tY t\ tZ d t[ d    tZ d t[ d   tY  | | | | | |E  }  f dn   }t^ || }do   }tV tW tX tY  td |  }  f dp   }t^ || }dq   }tV tW tX tY tY  |F |= td |  }  f dr   }t^ || }ds   }tV tW tX tY tZ d t[ d   tY  |/ |G |F |H td |  }  f dt   } t^ ||  }!  f du   }"tV tW tX tY tg tY  |I  }#t^ |#|" }$dv   }%tV tW tX tY  |J td |%  }&  f dw   }'t^ |&|' }(tV tW t[ d  ti th t[ d  tZ d t[ d   tY  | | |K  })  f dx   }*t^ |)|* }+tV tW t[ d  ti th t\ tZ d t[ d   tY  | | |L |M  },  f dy   }-t^ |,|- }.tV tW t[ d  ti th t\ tZ d t[ d   tY  | | |N |O  }/  f dz   }0t^ |/|0 }1tV tW th ti tX tZ d t[ d   tZ d t[ d   tY  | | |B |P  }2  f d{   }3t^ |2|3 }4d|   }5tV tW tX tY  td |5  }6  f d}   }7t^ |6|7 }8d~   }9tV tW tX tY  td |9  }:  f d   };t^ |:|; }<tV tW tY tZ d t[ d   tZ d t[ d   tZ d t[ d   tZ d& t[ d   tY tZ d t[ d   tZ d t[ d   tZ d t[ d   tZ d. t[ d   tZ d	 t[ d   tY  | | | |	 | | | |
 |Q |R |S |T  }=  f d   }>t^ |=|> }?tV tW tX ti tY tZ d t[ d   tZ d t[ d   tY tZ d7 t[ d   tZ d t[ d   t] tY  | | | | | |& |C |U 	 }@  f d   }At^ |@|A }Bd   }CtV tW tX tY  td |C  }D  f d   }Et^ |D|E }FtV tW tX tY   }G  f d   }Ht^ |G|H }I|X |[ |^ |a |d |g |j |n |r |v |z |~ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |||||||||!|$|(|+|.|1|4|8|<|?|B|F|IgD S(   Ni(U   t   cons147t   cons2002t   cons2t   cons3t   cons7t   cons4t   cons5t   cons386t   cons27t   cons50t   cons2003t   cons2004t   cons2005t   cons2006t   cons48t   cons125t   cons208t   cons34t   cons35t   cons36t   cons1099t   cons2007t   cons66t   cons21t   cons84t   cons1037t   cons1036t   cons38t   cons2008t   cons10t   cons2009t   cons2010t   cons2011t   cons209t   cons1831t   cons1244t   cons2012t   cons46t   cons2013t   cons2014t   cons2015t   cons2016t   cons52t   cons2017t   cons800t   cons2018t   cons17t   cons2019t   cons586t   cons2020t   cons2021t   cons2022t   cons2023t   cons2024t   cons2025t   cons2026t   cons2027t   cons2028t   cons667t   cons196t   cons2029t   cons840t   cons2030t   cons18t   cons2031t   cons148t   cons45t   cons2032t   cons1854t   cons1247t   cons261t   cons2033t   cons367t   cons2034t   cons67t   cons1479t   cons744t   cons1482t   cons165t   cons2035t   cons2036t   cons1676t   cons1255t   cons2037t   cons347t   bi   t   ai    t   cc            s}     j  d  t | t |   | | | | | t |   | | | | t |   t | | | | | |  |  |  S(   Ni  (   t   appendR  R$   R%   R   (   t   pt   uR  R  R  t   nt   x(   t   rubi(    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6931   s    R  c            sg     j  d  t | | | | | |  | | | | |  | t | | | | |  | |  |  S(   Ni  (   R  R  R   (   R  R  R  t   dR  R  R  t   q(   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6932   s    R  c	   	         ss     j  d  t | | | | | | |  | | | | | |  | t | | | | | |  | |  |  S(   Ni  (   R  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6933   s    t   et   gt   fR  i   t   Ct   Bt   Ac      
      sp     j  d  t | | t t | | | | |
  |	 |
 |
  |
 t | | |
  t | | |
   |
  S(   Ni  (   R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  t   FR  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6934   s    c
   
   
      s|     j  d  t | |  t t | | | | |  | | |  | t | | t d   t | | t d    |  S(   Ni  i   (   R  R  R*   R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6935   s    c      
      sn     j  d  t | | t t | | |
 | | | |
 |
  |
 t | | |
  t | | |
   |
  S(   Ni  (   R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6936   s    c
   
   
      sz     j  d  t | |  t t | | | | | | | |  | t |	 | t d   t | | t d    |  S(   Ni  i   (   R  R  R*   R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6937   s    c         S   sp   t  | t t t t f  r t Sy( t |  | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   t
   isinstancet   intR  t   floatR  t   FalseR  R5   R   t	   TypeErrort   AttributeErrort   True(   t   yR  R  R  t   res(    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6938   s    c            s?   t  |  | |  }   j d  t | t t |  |   |  S(   Ni  (   R  R  R  t   logR   (   R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6938   s    c         S   st   t  | t t t t f  r t Sy, t | |  | |  } t t |   } Wn t	 t
 f k
 re t SX| rp t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  t   wR  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6939   s    c            sG   t  | |  | |  }   j d  t | t t | |  |   |  S(   Ni  (   R  R  R  R  R   (   R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6939   s    c         S   sp   t  | t t t t f  r t Sy( t |  | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  t   mR  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6940   s    R  c            sL   t  |  | |  }   j d  t | |  | t d  | t d  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6940   s    c         S   s   t  | t t t t f  r t Sy9 t | |  | |  | | |  } t t |   } Wn t	 t
 f k
 rr t SX| r} t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   t   zR  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6941   s    #c            so   t  | |  | |  | | |  }   j d  t | | | t d  |  | t d  | t d  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6941   s    #c         S   sH   t  |  t t t t f  r t St | |   } t | | |   rD t St S(   N(	   R  R  R  R  R  R  R,  R   R  (   R  R  t   v(    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6942   s    c            s)   t  | |   }   j d  t | |   S(   Ni  (   R,  R  R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6942  s    c
   
         s     j  d  t | |	 t d  | | t d  | t t |  |	 t | | | |  | t | | | |  | |  |  |  S(   Ni  i   (   R  R  R  R   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6943  s    c
   
         s     j  d  t | |	 t d  | | t d  | t t |  | | | |	 t | | | |  | t | | | |  | |  |  |  S(   Ni   i   (   R  R  R  R   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6944  s    R  c            s?     j  d  t | | | | | | | | |  | |  S(   Ni!  (   R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6945  s    c
         S   sp   t  |	 t t t t f  r t Sy( t | | |	  }
 t t |
   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6946  s    c
            s`   t  | | |	  }
   j d  t |
 t t | | |	 | | | |	 | |	  |	 |  |	  S(   Ni"  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6946"  s    c         S   sp   t  | t t t t f  r t Sy( t | | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6947(  s    c            sp   t  | | |  }   j d  t | t t | | | | |	 | | |
 | | | | |  | |  |  S(   Ni#  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement69474  s    c         S   sp   t  | t t t t f  r t Sy( t | | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  t   hR  R  t   rR  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6948:  s    R  R  c            s   t  | | |  }   j d  t | t t | | | | | |
 | | | | | | |	 | | | |  | |  |  S(   Ni$  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6948F  s    c         S   sp   t  | t t t t f  r t Sy( t |  | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6949L  s    c            se   t  |  | |  }   j d  t | t | |  |  t | | t t | | |  | |   |  S(   Ni%  (   R  R  R  R   R*   (   R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6949X  s    c   	      S   sp   t  | t t t t f  r t Sy( t | | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6950^  s    c            sT   t  | | |  }   j d  t | t t | | | | |  |  | |  |  S(   Ni&  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6950j  s    c	      
   S   s   t  | t t t t f  r t Sy t d  }	 t d  }
 t | | |  | |  }
 t | | |  }	 t	 t
 t t |
 t | | |  | |     t
 t t |	 t | | |      } Wn t t f k
 r t SX| r t St S(   NR  R  (   R  R  R  R  R  R  R  R  R  R  R5   R   R	   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6951p  s    ]c	      	      s   t  d  }	 t  d  }
 t | | |  | |  }
 t | | |  }	   j d  t |	 |
 t t | | | | | | | |  | |  |  S(   NR  R  i'  (   R  R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6951  s    c
         S   sp   t  |	 t t t t f  r t Sy( t | | |	  }
 t t |
   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6952  s    R  c
      	      sj   t  | | |	  }
   j d  t |
 t t | | |	 | | |	 t d  | | |	  |	 |  |	  S(   Ni(  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6952  s    c         S   sp   t  | t t t t f  r t Sy( t | | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6953  s    c      
      sz   t  | | |  }   j d  t | t t | |  | |
 |	 | | |
 | | t d  |
 | |  | |  |  S(   Ni)  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6953  s    c         S   sp   t  |	 t t t t f  r t Sy( t | | |	  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6954  s    c      
      sn   t  | | |	  }   j d  t | t t |
 |  |	 | | | |	 t d  | | |	  |	 |  |	  S(   Ni*  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6954  s    c      
   S   s   t  | t t t t f  r t Sy t d  } t d  } t | | |  | |  } t | | |  } t	 t
 t t | t | | |  | |     t
 t t | t | | |      } Wn t t f k
 r t SX| r t St S(   NR  R  (   R  R  R  R  R  R  R  R  R  R  R5   R   R	   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6955  s    ]c      
      s   t  d  } t  d  } t | | |  | |  } t | | |  }   j d  t | | t t | | |	 | | |
 | | t d  |
 | |  | |  |  S(   NR  R  i+  i   (   R  R  R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6955  s    c      
   S   s   t  | t t t t f  r t Sy t d  } t d  } t | | | | |  } t | | |  } t	 t
 t t | t | | | | |     t
 t t | t | | |      } Wn t t f k
 r t SX| r t St S(   NR  R  (   R  R  R  R  R  R  R  R  R  R  R5   R   R	   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6956  s    ]c      
      s   t  d  } t  d  } t | | | | |  } t | | |  }   j d  t | | t t | | | |  | | | | | | |
 | t d  | | |  | |  |  S(   NR  R  i,  i   (   R  R  R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6956  s    c      
   S   s   t  | t t t t f  r t Sy t d  } t d  } t | | | | |  } t | | |  } t	 t
 t t | t | | | | |     t
 t t | t | | |      } Wn t t f k
 r t SX| r t St S(   NR  R  (   R  R  R  R  R  R  R  R  R  R  R5   R   R	   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6957  s    ]c      
      s   t  d  } t  d  } t | | | | |  } t | | |  }   j d  t | | t t | | | |  | |
 | |	 | t d  |
 | |  | |  |  S(   NR  R  i-  i   (   R  R  R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6957  s    c         S   sp   t  |
 t t t t f  r t Sy( t | | |
  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6958  s    c      	      sh   t  | | |
  }   j d  t | t t | | |
 |	 | | | |
 |	 | |
  |
 |  |
  S(   Ni.  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6958  s    c         S   sp   t  | t t t t f  r t Sy( t | | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6959  s    c      	      s|   t  | | |  }   j d  t | t t |
 | | | | |	 | | | | | | | | | |  | |  |  S(   Ni/  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6959$  s    c         S   sp   t  | t t t t f  r t Sy( t |  | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6960*  s    c            s>   t  |  | |  }   j d  t | |  | t |  |  S(   Ni0  (   R  R  R  R  (   R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement69606  s    c         S   sp   t  | t t t t f  r t Sy( t |  | |  } t t |   } Wn t	 t
 f k
 ra t SX| rl t St S(   N(   R  R  R  R  R  R  R  R5   R   R  R  R  (   R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6961<  s    c            sP   t  |  | |  }   j d  t | t t | | | | |  | |   |  S(   Ni1  (   R  R  R  R*   R   (   R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6961H  s    c   	      S   s^   t  | t t t t f  r t S| |  t | |  | t |  |  } t | |  rZ t St S(   N(	   R  R  R  R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6962N  s    (c   	         sn   | |  t  | |  | t  |  |  }   j d  t | t t | | | | | |  | |  |  |  S(   Ni2  (   R  R  R  R*   R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6962V  s    (c
         S   sf   t  | t t t t f  r t S| | | t |  |  |	 |  t | |  }
 t |
 |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6963\  s    0R  c
            s   | | | t  |  |  |	 |  t  | |  }
   j d  t |
 | | t d  t t | | | | | t d  | |  | |  | t d  |  |  S(   Ni3  i   (   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6963d  s    0c         S   sf   t  | t t t t f  r t S| | | t |  |  |
 |  t | |  } t | |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  t   sR  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6964j  s    0R  c            s   | | | t  |  |  |
 |  t  | |  }   j d  t | | | t d  t t | | | | | t d  | |  | |  | t d  | |	 t d   |  S(   Ni4  i   (   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6964r  s    0c	   
      S   sf   t  | t t t t f  r t S| | | t |  |  | |  t | |  }	 t |	 |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6965x  s    0c	   
   
      s   | | | t  |  |  | |  t  | |  }	   j d  t |	 | t t | | | | | |  | |  | | | t d   |  S(   Ni5  i   (   R  R  R  R*   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6965  s    0c
         S   sf   t  | t t t t f  r t S| | | t |  |  |	 |  t | |  }
 t |
 |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6966  s    0c
      	      s   | | | t  |  |  |	 |  t  | |  }
   j d  t |
 |	 t t | | | |	 | |  | |  | | | t d  |  |  S(   Ni6  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6966  s    0c
         S   sf   t  | t t t t f  r t S| | | t |  |  |	 |  t | |  }
 t |
 |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6967  s    0c
            s   | | | t  |  |  |	 |  t  | |  }
   j d  t |
 |	 | t d  t t | | | |	 | t d  | |  | |  | | t d  | | t d   |  S(   Ni7  i   (   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6967  s    0c         S   sf   t  | t t t t f  r t S| | | t |  |  |
 |  t | |  } t | |  rb t St S(   N(	   R  R  R  R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6968  s    0c            s   | | | t  |  |  |
 |  t  | |  }   j d  t | |
 |	 t d  t t | | | |
 |	 t d  | |  | |  | | | t d  | |	 t d   |  S(   Ni8  i   (   R  R  R  R  R*   R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6968  s    0c      	      sn     j  d  t t d  | t d  t t t |  | t d  | |   |   |  |  | t d   |   S(   Ni9  i   (   R  R  R  R*   R   R  (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6969  s    c         S   s   t  |  t t t t f  r t SyI t | |   } t t t	 |   t
 | t | t d   |    } Wn t t f k
 r t SX| r t St S(   Ni   (   R  R  R  R  R  R  RN  R  R5   R   R   R  R  R  R  R  (   R  R  t   lstR  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6970  s    :c            s   t  | |   }   j d  t t | t d   t | t d   t t t | t d   |   |  t | t d   t d  t | t d    |   S(   Ni:  i   i   i   i   (   RN  R  R  R  R  R*   R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6970  s    c         S   sm   t  |  t t t t f  r t Sy% t | |   } t t |   } Wn t	 t
 f k
 r^ t SX| ri t St S(   N(   R  R  R  R  R  R  R   R5   R   R  R  R  (   R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6971  s    c            s   t  | |   }   j d  t t | t d   t | t d   t t t | t d   |   |  t | t d   t d  t | t d    |   S(   Ni;  i   i   i   i   (   R   R  R  R  R  R*   R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6971  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  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6972  s    c            s     j  d  t | t |  |  | t |  | | t |  | |  | | | t |  t | |  | | | | | |  |  S(   Ni=  (   R  R  R$   R%   R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6973  s    c            se     j  d  t | t |  |  | t |  | |  | t |  t | |  | | |  |  S(   Ni>  (   R  R  R$   R%   R   (   R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6974  s    c            s     j  d  t t | | t d  t | | | |  t | | | |   t | | | |  | | | | |  |  |  S(   Ni?  i   (   R  R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6975  s    c            s     j  d  t |  | t |  | | |  | t |  | |  | | t |  t | |  | | | |  | | | |  |  S(   Ni@  (   R  R  R%   R   (   R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6976  s    c            s     j  d  t |  | t |  | | |  | | | t |  | |  | | | | t |  t | |  | | | |  | | | | | |  |  S(   NiA  (   R  R  R%   R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6977  s    c         S   s   t  | t t t t f  r t S| | t |  | | | | | t |  | | | | | | t |  } t t | t	 d    r t
 St S(   Ni   (   R  R  R  R  R  R  R%   R5   R   R  R  (   R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6978  s    Wc      	      s   | | t  |  | | | | | t  |  | | | | | | t  |  }   j d  t | t |  | | | | | | | | | |  |  S(   NiB  (   R%   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6978  s    Wc         S   sR   t  | t t t t f  r t St |  | | | | |  } t |  rN t St S(   N(	   R  R  R  R  R  R  R   R(   R  (   R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6979  s    c            s9   t  |  | | | | |  }   j d  t | |  S(   NiC  (   R   R  R   (   R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6979  s    c            sb     j  d  t t d  |  | |  t | | t d  | | | t d  |  |  |  S(   NiD  i   i   (   R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6980  s    c            s     j  d  t | t d  | | | t d  |  | | | | | | t d  | |  t | | t d  | | | t d  |  |  |  S(   NiE  i   (   R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6981  s    c         S   sh   t  | t t t t f  r t St |  | | | | | | t d  | |  } t |  rd t	 St S(   Ni   (
   R  R  R  R  R  R  R   R  R(   R  (   R  R  R  R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6982  s    5c            sO   t  |  | | | | | | t d  | |  }   j d  t | |  S(   Ni   iF  (   R   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6982%  s    5c            sv     j  d  t |  | | | | t | | |  | t d  | t d  | | t d  | | | |  S(   NiG  i   (   R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6983,  s    c         S   sm   t  |  t t t t f  r t Sy% t | |   } t t |   } Wn t	 t
 f k
 r^ t SX| ri t St S(   N(   R  R  R  R  R  R  R!  R5   R   R  R  R  (   R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With69840  s    c      
      s   t  | |   }   j d  t t d  t | t d   t t t | t d   |   |  |  t | t d   t | t d    |   S(   NiH  i   i   i   (   R!  R  R  R  R  R*   R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6984<  s    c         S   s   t  |  t t t t f  r t SyL t | t d  |   } t t	 t
 |   t t | t d     } Wn t t f k
 r t SX| r t St S(   Ni    i   (   R  R  R  R  R  R  Rz  R  R  R5   R   R   R  R  R  R  (   R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6985B  s    4c      
      s   t  | t d  |   }   j d  t t d  t | t d   t t t t | t d   |  |   |   |  |  t | t d   t | t d    |   S(   Ni    iI  i   i   i   (   Rz  R  R  R  R  R*   R   R"  (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6985N  s    c         S   s   t  |  t t t t f  r t Sy_ t | | t d  |   } t t	 t
 |   t | t | t d   t d    } Wn t t f k
 r t SX| r t St S(   Ni   i   i(   R  R  R  R  R  R  Rz  R  R  R5   R   R   R  R  R  R  (   R  R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6986T  s    Cc      
      s   t  | | t d  |   }   j d  t t d  t | t d   t t t t | t d   |  |   |   |  |  t | t d   t | t d    |   S(   Ni   iJ  i   i   (   Rz  R  R  R  R  R*   R   R"  (   R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6986`  s    c            s   t  |  }   j d  t | t t |  | | t d  t d  t | t |  |  |   |   |  |  t d  |  |   S(   NiK  i   i(   R3   R  R  R*   R   R  R   R  (   R  R  R  t   k(   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6987f  s    c         S   sm   t  |  t t t t f  r t Sy% t | |   } t t |   } Wn t	 t
 f k
 r^ t SX| ri t St S(   N(   R  R  R  R  R  R  R~  R5   R   R  R  R  (   R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6988l  s    c      	      se   t  | |   }   j d  t t d  t t t | t d   |   |  t | t d    |   S(   NiL  i   i   (   R~  R  R  R  R*   R   R  (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6988x  s    c            s     j  d  t t d  t d  | t t t d  |  t | | t d   t d   |  |  t t d  t d  | t t t d  |  t | | t d   t d   |  |  S(   NiM  i   i   (   R  R  R  R   R   R  (   R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6989  s    c            s     j  d  t t d  | | t t t t d  t d  t d  t d  t | |  t d  t | | | t d    |  t t t d  | t d    |  S(   NiN  i   i   ii   (	   R  R  R  R  R   R   R  R  R   (   R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6990  s    c            s     j  d  t t d  | | t t t t d  t d  t d  t d  t | |  t | | |   |  t t t d  |   |  S(   NiO  i   ii   (	   R  R  R  R  R   R   R  R  R   (   R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6991  s    c            sQ     j  d  t t t t |  | |  | | | | |  t | |   |  S(   NiP  (   R  R   R   R   R  R  (   R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6992  s    c         S   sE   t  |  t t t t f  r t St | |   } t | |  rA t St S(   N(	   R  R  R  R  R  R  R"  R  R  (   R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6993  s    c            s)   t  | |   }   j d  t | |   S(   NiQ  (   R"  R  R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6993  s    c         S   sB   t  |  t t t t f  r t St | |   } t |  r> t St S(   N(	   R  R  R  R  R  R  R   R(   R  (   R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6994  s    c            s)   t  | |   }   j d  t | |   S(   NiR  (   R   R  R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6994  s    c
   
         sc     j  d  t | | |  | | | | |  | | | | |	 t | | | |  |  |  S(   NiS  (   R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6995  s    c            s     j  d  t t d  | |  t d  d t | | | | | | t d  |  | t d  | | | t | | t d  | | | t d  |  |  |  S(   NiT  i   i   i   (   R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6996  s    c         S   sm   t  |  t t t t f  r t Sy% t | |   } t t |   } Wn t	 t
 f k
 r^ t SX| ri t St S(   N(   R  R  R  R  R  R  RN  R5   R   R  R  R  (   R  R  R  R  (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   With6997  s    c            s   t  | |   }   j d  t t | t d   t | t d   t t t | t d   |   |  t | t d   t d  t | t d    |   S(   NiU  i   i   i   i   (   RN  R  R  R  R  R*   R   (   R  R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6997  s    c            s     j  d  t | |   S(   NiV  (   R  R   (   R  R  (   R  (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   replacement6998  s    (k   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  t   u_t   x_R  R  t   n_t   p_R   t   d_t   q_t   F_R  t   y_R   t   w_t   z_t   m_t   v_t   a_t   A_(J  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~  t   pattern6931R  t   rule6931t   pattern6932R  t   rule6932t   pattern6933R  t   rule6933t   pattern6934R  t   rule6934t   pattern6935R  t   rule6935t   pattern6936R  t   rule6936t   pattern6937R  t   rule6937R  t   pattern6938R  t   rule6938R  t   pattern6939R  t   rule6939R  t   pattern6940R  t   rule6940R  t   pattern6941R  t   rule6941R  t   pattern6942R  t   rule6942t   pattern6943R  t   rule6943t   pattern6944R  t   rule6944t   pattern6945R  t   rule6945R  t   pattern6946R  t   rule6946R  t   pattern6947R  t   rule6947R  t   pattern6948R  t   rule6948R  t   pattern6949R  t   rule6949R  t   pattern6950R  t   rule6950R  t   pattern6951R  t   rule6951R  t   pattern6952R  t   rule6952R  t   pattern6953R  t   rule6953R  t   pattern6954R  t   rule6954R  t   pattern6955R  t   rule6955R  t   pattern6956R  t   rule6956R  t   pattern6957R  t   rule6957R  t   pattern6958R  t   rule6958R  t   pattern6959R  t   rule6959R  t   pattern6960R  t   rule6960R  t   pattern6961R  t   rule6961R  t   pattern6962R  t   rule6962R  t   pattern6963R  t   rule6963R  t   pattern6964R  t   rule6964R  t   pattern6965R  t   rule6965R  t   pattern6966R  t   rule6966R  t   pattern6967R  t   rule6967R  t   pattern6968R  t   rule6968t   pattern6969R  t   rule6969R  t   pattern6970R  t   rule6970R  t   pattern6971R  t   rule6971t   pattern6972R  t   rule6972t   pattern6973R  t   rule6973t   pattern6974R  t   rule6974t   pattern6975R  t   rule6975t   pattern6976R  t   rule6976t   pattern6977R  t   rule6977R  t   pattern6978R  t   rule6978R  t   pattern6979R  t   rule6979t   pattern6980R  t   rule6980t   pattern6981R  t   rule6981R  t   pattern6982R  t   rule6982t   pattern6983R  t   rule6983R  t   pattern6984R  t   rule6984R  t   pattern6985R  t   rule6985R  t   pattern6986R  t   rule6986R   t   pattern6987t   rule6987R  t   pattern6988R  t   rule6988t   pattern6989R  t   rule6989t   pattern6990R  t   rule6990t   pattern6991R  t   rule6991t   pattern6992R  t   rule6992R  t   pattern6993R  t   rule6993R	  t   pattern6994R
  t   rule6994t   pattern6995R  t   rule6995t   pattern6996R  t   rule6996R  t   pattern6997R  t   rule6997t   pattern6998R  t   rule6998(    (   R  sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   miscellaneous_integration   s     
o :  : 	"	&	;	U	p			 @	X	n									 	,	F							5		~ghk		F			(	A 	!IFFO			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  t   expR  R  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  t   Pit   iR  t   B_t   C_R  t   G_t   H_R  t   b_t   c_R  t   e_t   f_t   g_t   h_t   i_t   j_t   k_t   l_R  R  R  R  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_t   n1_t   n2_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  R  R  R  t	   _UseGammat	   ShowStepst   Nonet   StepCounterR  (    (    (    sS   lib/python2.7/site-packages/sympy/integrals/rubi/rules/miscellaneous_integration.pyt   <module>   s>   "           1nj:R4|'	