
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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   ~        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 } t t t t t d t d   t d t d   t d 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 t t d t d   t d t d   t d t d   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  | | | |  }   f 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 d   t d t d   t d	 t d   t d
 t d    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 d t d   t d t d   t d	 t d   t d
 t d     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 d 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 t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t t  |
 | | | | | | | | |  }   f d   } 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 d t d   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 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 d	 t d   t d
 t d    t  |
 | | | | | | | | | |  }   f d   } 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 d t d   t d	 t d   t d
 t d    t d t d   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 d   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 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 d t d    t  | | | | | | | | | |  }   f d   } 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  | | | | | | | | | |  }   f d   } t | |  } t 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 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 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 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 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 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 d   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 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 d   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 d
 t d    t d t d   t  |
 | | | | | | | | | | | |  }   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 d t d   t  | | | | | |  }   f d#   } 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 d t d   t d t d   t  |
 | | | | | | | |  
 }   f d$   } t | |  } t t t d t d   t d t d   t t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t d t d   t t d t d   t d t d   t  |
 | | | | | | | | | |! |"  }   f d%   } t | |  } t t t t d t d   t d t d   t d t d   t d t d   t d t d   t t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t  |
 | | | | | | | | | | |! |  }   f d&   } t | |  } t t t d t d   t d t d   t t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t t t d t d   t d t d   t d'  t  |
 | | | | | | | | | |! | |	  }   f d(   } t | |  } t t t t d t d   t d t d   t d t d   t d t d   t d t d   t t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t t  |
 | | | | | | | | | | |! | |	 | |# |$  }   f d)   } t | |  } t t t t d t d   t d t d   t d t d   t d t d   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 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 d   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 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 d   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 d
 t d    t t  |
 | | | | | | | | | | |! |%  }   f d,   } t | |  } t t t t d t d   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  |
 | | | | | | | |( |)  }   f d-   } t | |  } t 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 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 d t d   t d t d    t t d t d   t d t d   t t d/ t d   t d0 t d   t  | | | | | |, |- | |+ 
 }   f d1   } t | |  } t t t t d t d   t t d
 t d   t t d t d   t d t d    t t d t d   t d t d   t t d/ t d   t d0 t d   t  |
 | | | | | | |, |- | |+  }   f d2   } t | |  }   f d3   } t t t t d/ t d   t d0 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 d	 t d   t d
 t d    t t d t d   t d t d   t  |
 | | | | | | | |, |- | | | |.  } t | |  } t t t t d/ t d   t d0 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 d t d   t  |
 | | | | | | |, |- | | |% |/  }   f d4   } t | |  } d5   } t t t t d/ t d   t d0 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 d	 t d   t d
 t d    t d t d   t t d t d   t d t d   t  |
 | | | | | | | |, |- | | |0 |" t |   }   f d6   } t | |  } t t t t d/ t d   t d0 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 d	 t d   t d
 t d    t d t d   t t d t d   t d t d   t  |
 | | | | | | | |, |- | | | | |1  }   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  | | | | | |2 |3  }  f d8   }t || }t t t d t d   t d t d   t t d
 t d   t t d t d   t d t d    t t t d'  t d t d   t  | | | | | |2 |4 |5 	 }  f d9   }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 d t d   t d	 t d   t d
 t d    t t d'  t d0 t d   t t d t d   t d t d   t  |
 | | | | | | | |, | | |6  }  f d:   }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 d
 t d    t t t d'  t d0 t d   t  |
 | | | | | | |, | | |7  }
  f d;   }t |
| }  f 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 d t d   t d	 t d   t d
 t d    t t t t d'  t d t d    t  |
 | | | | | | | | | |8  }t || }  f 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 d t d   t d	 t d   t d
 t d    t t t t d> t d    t t t t d? t d    t  |
 | | | | | |< |= |> |? | | |9 |: |;  }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 d t d   t d	 t d   t d
 t d    t t t t d'  t d t d    t  |
 | | | | | | | | | |@  }  f d@   }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 d t d   t d	 t d   t d
 t d    t t t t d> t d    t t t t d? t d    t  |
 | | | | | |< |= |> |? | | |9  }  f dA   }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 d t d   t d	 t d   t d
 t d    t d t d   t t t dB t d   t d/ t d   t d0 t d    t t d t d   t d t d   t  |
 | | | | | | | |, |- |B | | | |	 |A  }  f dC   }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 d t d   t d	 t d   t d
 t d    t d t d   t t t dB t d   t d/ t d   t d t d   t d0 t d   t d   t t d t d   t d t d   t  |
 | | | | | | | |, |- |B | | | | |	 |C  }  f dD   }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 d t d   t d	 t d   t d
 t d    t d t d   t t t t dB t d   t d/ t d   t d t d   t d0 t d    t t d t d   t d t d   t  |
 | | | | | | | |, |- |B | | | |D | |	 |C  }  f dE   } t ||  }!  f dF   }"t t 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 t d   t d	 t d   t d
 t d    t dG t d   t  |
 | | | | | | | | | |E |% |F  }#t |#|" }$t t 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 d   t d
 t d    t d t d   t t  |
 | | | | | | | | | |"  }%  f dH   }&t |%|& }'t t t d t d   t d t d   t t t t t t dI t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t d t d   t t  |
 | | | | | | | | | |G |"  }(  f dJ   })t |(|) }*t t t t dK t d   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 d	 t d   t d
 t d    t d t d   t  |
 | | | | | | | | |D |H  }+  f dL   },t |+|, }-t t t t dK 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 t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t d t d   t  |
 | | | | | | | | | | | |D |H  }.  f dM   }/t |.|/ }0  f dN   }1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  |
 | | | | | |I  }2t |2|1 }3t t t t t t d t d   t d t d   t d
 t d    t t t t d t d   t d t d   t  |
 | | | | | |J |K 	 }4  f dO   }5t |4|5 }6t t t t t t t d t d   t d t d   t d t d   t d
 t d    t t t t d t d   t d t d   t  |
 | | | | | |J |K 	 }7  f dP   }8t |7|8 }9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 d t d   t d	 t d   t d
 t d    t d t d   t  |
 | | | | | | | | |E  }:  f dQ   };t |:|; }<dR   }=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 d t d   t d	 t d   t d
 t d    t d t d   t  |
 | | | | | | | |L |" t |=  }>  f dS   }?t |>|? }@dT   }A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 d t d   t d	 t d   t d
 t d    t d t d   t  |
 | | | | | | | |L |" t |A  }B  f dU   }Ct |B|C }Dt t t d t d   t d t d   t t t d'  t d t d   t t d t d   t d t d   t d t d   t d t d   t d	 t d   t d
 t d    t d t d   t dV t d   t  |
 | | | | | | | | |M |N  }E  f dW   }Ft |E|F }G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 d
 t d    t d t d   t dV t d   t  |
 | | | | | | |O |P 
 }H  f dX   }It |H|I }Jt t t t t d t d   t d
 t d   t t d t d   t t d t d    t dI t d   t  |
 | | | | | |D |Q 	 }K  f dY   }Lt |K|L }Mt t t t d t d   t t t d t d   t d
 t d   t t d t d   t t d t d    t dI t d   t  |
 | | | | | | |D | |R  }N  f dZ   }Ot |N|O }Pt t t dV t d   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 d t d    t d t d   t  |
 | | | | | | |T |S 
 }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 d t d   t d
 t d   t t d[ t d   t d t d   t d t d    t d t d   t  |
 | | | | | |T |X |U |V |W  }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 d t d   t d
 t d    t t d t d   t d t d   t  |
 | | | | | | |V |Y |Z  }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 d t d   t d
 t d   t t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d t d   t  |
 | | | | | | | |T |X |U |V |Y |W  }Z  f d`   }[t |Z|[ }\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 t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d t d   t  |
 | | | | | | | |T |X |U |V |[ |W  }]  f da   }^t |]|^ }_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 t d[ t d   t d t d   t d t d    t t d t d   t d t d   t  |
 | | | | | | | |T |X |U |V |\  }`  f db   }at |`|a }b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 t d[ t d   t d t d   t d t d    t t t d t d   t d t d   t  |
 | | | | | | | |T |X |U |V |\ |N |]  }c  f dc   }dt |c|d }et t t d  t 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 d
 t d    t  |
 | | | | | | |V |Y 
 }f  f dd   }gt |f|g }ht t t d  t 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 d
 t d   t t d[ t d   t d t d   t d t d    t  |
 | | | | | | | |T |X |U |V |Y  }i  f de   }jt |i|j }kt t t d  t 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 d
 t d   t t d[ t d   t d t d   t d t d    t  |
 | | | | | | | |T |X |U |V |[  }l  f df   }mt |l|m }n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 t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d t d   t d'  t  |
 | | | | | | | |T |X |U |V |^ |W  }o  f dg   }pt |o|p }q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 t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d t d   t d'  t  |
 | | | | | | | |T |X |U |V |\ |W  }r  f dh   }st |r|s }t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 t d[ t d   t d t d   t d t d    t t t d t d   t d t d   t di  t  |
 | | | | | | | | |T |X |U |V |^ |Y  }u  f dj   }vt |u|v }w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 t d[ t d   t d t d   t d t d    t t t d t d   t d t d   t di  t  |
 | | | | | | | | |T |X |U |V |\ |[  }x  f dk   }yt |x|y }z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 d t d   t d
 t d   t t d[ t d   t d t d   t d t d    t d t d   t  |
 | | | | | | | |T |X |U |V |W |0 |  }{  f dl   }|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 dm t d   t t t t d t d    t d t d   t  |
 | | | | | |b |_ |V | |` |a  }~  f dn   }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 dm t d   t t  t d t d   t  |
 | | | |b |_ |V | |` |a  }  f do   }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 dm t d   t t t t d t d    t  |
 | | | | | |b |_ |V |  }  f dp   }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 dm t d   t t  t  |
 | | | |b |_ |V | 	 }  f dq   }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 dm t d   t t t t d t d    t d t d   t  |
 | | | | | |b |_ |V | |` |c  }  f dr   }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 dm t d   t t  t d t d   t  |
 | | | |b |_ |V | |` |c  }  f ds   }t || }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 t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d
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 | | | | | | | |T |X |U |V |^ |Y  }  f dt   }t || }t t t t t d t d   t d t d   t d t d   t t d t d   t d
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 | | | | | | |V |^ |\ |d  }  f du   }t || }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 t d[ t d   t d t d   t d t d    t d t d   t t d t d   t d
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 | | | | | | | |T |X |U |V |^ |\ |W  }  f dv   }t || }t t t t t d t d   t d t d   t d t d   t t d t d   t d
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 | | | | | | |e |f 
 }  f dw   }t || }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 t d[ t d   t d t d   t d t d    t d t d   t t d'  t d t d   t t d t d   t d t d   t  |
 | | | | | | | | | |T |X |U |V |g  }  f dx   }t || }t t t t t d t d   t d t d   t d] t d   t t d t d   t d
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 | | | | | |i |b |V |` |a  }  f d{   }t || }t t t t  t d t d   t t  t t d t d   t d t d   t t d t d   t d
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 }  f d|   }t || }  f d}   }t t t t  t t t t d t d    t t t d t d   t d t d   t t d t d   t d
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 }t || }t t t t  t t t t d t d    t d t d   t t d t d   t d t d   t t d t d   t d
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 }  f d   }t || }  f d   }t t t t  t t t t d t d    t t t d t d   t d t d   t t d t d   t d
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 | | | | |k |b |V |` |c  }  f d   }t || }t t t t t  t t t t d t d    t t t d t d   t d t d   t t d t d   t d
 t d   t  |
 | | | | | | |l |b |V |` |]  }  f d   }t || }t t t t t  t t  t t t d t d   t d t d   t t d t d   t d
 t d   t  |
 | | | | |l |b |V |` |]  }  f d   }t || }t t t t t  t t t t d t d    t t t d t d   t d t d   t t d t d   t d
 t d   t  |
 | | | | | | |l |b |V |` |c  }  f d   }t || }t t t t t  t t  t t t d t d   t d t d   t t d t d   t d
 t d   t  |
 | | | | |l |b |V |` |c  }  f d   }t || }t t t dV t d   t t t d t d   t d t d   t d] t d   t t d t d   t d
 t d   t t d[ t d   t d t d   t d t d    t d t d   t t d'  t d t d   t t d t d   t d t d   t  |
 | | | | | | | | | |T |X |U |V |m |n  }  f d   }t || }t t t dV t d   t t t d t d   t d t d   t d] t d   t t d t d   t d
 t d   t t d[ t d   t d t d   t d t d    t d t d   t t d'  t d t d   t d t d   t  |
 | | | | | | | | |T |X |U |V |m |o  }  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 d
 t d   t t d[ t d   t d t d   t d t d    t t t d'  t d t d   t t d t d   t  |
 | | | | |T | | | | |X |U  }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 t d[ t d   t d t d   t d t d    t t t d'  t d t d   t  |
 | | | | |T | | | |X |U  }t || }d   }t 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 t d[ t d   t d t d   t d t d    t d t d   t  |
 | | | | | |T |X |U |L |W t |  }  f d   }t || }d   }t t t dV t d   t t  t d t d   t  | |p |q t |  }  f d   }t || }t t t t t t d t d   t d t d   t d t d   t d
 t d    t  |
 | | | | |r  }  f d   }t || }t t t t t d t d   t d
 t d    t  | | |s |t  }  f d   }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 t d t d   t d t d   t  |
 | | | | | | | | |u  }  f d   }t || }t 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 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 d t d   t d t d   t t t d t d   t d
 t d    t  |
 | | | | |v |s |w 	 }  f d   }t || }  f 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 d   t d
 t d    t t t d t d   t d t d    t d t d   t  |
 | | | | | | | | |%  }t || }  f 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 d   t d
 t d    t t d'  t d t d   t d t d   t  |
 | | | | | | | |x 
 }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 t  |
 | | | | | |"  }  f d   }t || } t t t t d t d   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 t  |
 | | | | | |" |y 	 }  f d   }t || }t t t t d t d   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 t  |
 | | | | | | |" |z 
 }  f d   }t || }d   }t t t t t  t  t |  }  f d   }	t ||	 }
d   }t t t t d t d   t d t d   t t  t t  t  |
 | |{ t |  }  f d   }t || }t t t t t t d t d   t d t d   t t d t d   t d t d   t d
 t d    t  |
 | | | | | | || 	 }  f d   }t || }t t t t t t d t d   t d t d   t d 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 t t d t d   t t d t d   t d 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 t t d t d   t d
 t d    t d t d   t  |
 | | | |L |"  }  f d   }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 d t d   t d t d   t  |
 | | | | | |L |" 	 }  f d   }t || }t 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  |
 | | | | | | |L |" |~ |  }  f 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  | | | | |L |  }"t |"|! }#  f d   }$t t t t t d t d   t d
 t d    t t  | | | |  }%t |%|$ }&d   }'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  |
 | | | |L | |" t |' 	 }(  f d   })t |(|) }*d   }+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  |
 | | | |L | |" t |+ 	 },  f d   }-t |,|- }.d   }/t t t t d t d   t d t d   t t  t  |
 | |L t |/  }0  f d   }1t |0|1 }2t t t t d t d   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 d t d   t d   t  | |
 | | | | | | | |'  }3  f d   }4t |3|4 }5t t t 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 d   t d t d    t  | |
 | | | | | | | | |' |  }6  f d   }7t |6|7 }8t t t t t d t d   t t t d'  t d
 t d   t t d t d   t d t d    t d t d   t d t d    t  |
 | | | | | |  }9  f d   }:t |9|: };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 d    t  |
 | | | | |  }<  f d   }=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 t d t d   t d t d    t d t d   t d t d    t  |
 | | | | | | | | | |  }?  f d   }@t |?|@ }A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 d    t d t d   t d t d    t  |
 | | | | | | | | |  }B  f d   }Ct |B|C }Dt t t d t d   t t t  t d t d   t t d t d   t d t d    t  | | | | | |  }E  f d   }Ft |E|F }Gt t t t  t  |{  }H  f d   }It |H|I }Jt t t t  t t d t d   t d t d   t  |
 | | |  }K  f d   }Lt |K|L }Mt t t t d t d   t d t d   t d t d   t t  t  |
 | | |{ |  }N  f d   }Ot |N|O }P  f d   }Qt t t t  t t  | |{  }Rt |R|Q }St t t t t d t d   t t  t  |
 |{  }T  f d   }Ut |T|U }Vd   }Wt t t t t  t  |{ t |W  }X  f d   }Yt |X|Y }Zt t t t  t t  t  | |  }[  f d   }\t |[|\ }]d   }^t t t t t  t t  t  | | t |^  }_  f d   }`t |_|` }at t t t d t d   t t t d t d   t d t d    t d t d    t  |
 | | | |  }b  f d   }ct |b|c }dt t t t d t d   t t t d t d   t d t d    t d t d    t t  |
 | | | |  }e  f d   }ft |e|f }g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 d    t  |
 | | | | |  }h  f d   }it |h|i }j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 t t d t d   t d
 t d     t  |
 | | | | | |  }k  f d   }lt |k|l }mt t t t d t d   t t  t  |
 | |  }n  f d   }ot |n|o }pd   }qt t t t  | t |q  }r  f d   }st |r|s }tt t t dV t d   t t t   t   }u  f d   }vt |u|v }wt t t t d t d   t t d t d   t t  t d t d   t d t d   t dV t d   t  |
 | | |N  }x  f d   }yt |x|y }z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 d t d   t d	 t d   t d
 t d    t t dV t d   t  |
 | | | | | | | | |  }{  f d   }|t |{|| }}| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |||	||||||||!|$|'|*|-|0|3|6|9|<|@|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}||||||||||||||||||||||||||||||||||||||||||| |||
||||||| |#|&|*|.|2|5|8|;|>|A|D|G|J|M|P|S|V|Z|]|a|d|g|j|m|p|t|w|z|}g S(   Ni(   t   cons1156t   cons7t   cons27t   cons48t   cons125t   cons5t   cons50t   cons87t   cons88t   cons2t   cons3t   cons1157t   cons415t   cons1158t   cons1159t   cons89t   cons543t   cons1160t   cons208t   cons209t   cons584t   cons4t   cons66t   cons21t   cons1161t   cons1162t   cons1163t   cons1164t   cons1165t   cons1166t   cons1167t   cons1168t   cons1169t   cons148t   cons1170t   cons1171t   cons62t   cons93t   cons168t   cons810t   cons811t   cons222t   cons1172t   cons224t   cons796t   cons79t   cons1173t   cons17t   cons1174t   cons1175t   cons1176t   cons1177t   cons1178t   cons1179t   cons1180t   cons1181t   cons1182t   cons1183t   cons1184t   cons1185t   cons1186t   cons1187t   cons1188t   cons1189t   cons1190t   cons797t   cons1191t   cons52t   cons925t   cons1192t   cons1193t   cons1194t   cons1195t   cons1196t   cons1197t   cons1198t   cons1199t   cons38t   cons552t   cons1200t   cons1201t   cons1202t   cons25t   cons652t   cons1203t   cons71t   cons128t   cons1204t   cons1205t   cons1206t   cons1207t   cons1208t   cons146t   cons1209t   cons1210t   cons13t   cons163t   cons1211t   cons137t   cons1212t   cons1213t   cons1214t   cons1215t   cons1216t   cons1217t   cons1218t   cons1219t   cons1220t   cons1221t   cons1222t   cons70t   cons1223t   cons1224t   cons806t   cons840t   cons1225t   cons1226t   cons68t   cons1125t   cons1227t   cons1228t   cons1229t   cons1230t   cons463t   cons1231t   cons1232t   cons1233t   cons1234t   cons1235t   cons1236t   cons31t   cons1099t   cons1237t   cons1055t   cons515t   cons816t   cons817t   cons1238t   cons1239t   cons1240t   cons1241t   cons1242t   cons1243t   cons1244t   cons1245t   cons34t   cons35t   cons1246t   cons1247t   cons1248t   fi   t   ei    t   pt   dt   qt   cc            s]     j  d  t | | | t | | | | | |  |  | |  t |  | | |  S(   Ni  (   t   appendR  t   log(   R  R  R  R  t   xR  R  (   t   rubi(    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2006   s    t   at   bc
   
         s     j  d  t | | |  | t | | t | | |	 | | |  |  | t d  |  |  t | | t | | |	 | | |  |  | |	 | | | |  S(   Ni  i(   R  R  R   R  R  R  (
   R  R  R  R  R  R  t   nR  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2007   s    c            s4     j  d  t t |  | | |  |  | |  S(   Ni  (   R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2008   s    c	   	         s     j  d  t | | | | | |  | t d  |  | | | | t | | t | | | | | |  |  | |  |  t | | |  |  | | |  | |  S(   Ni  i   (   R  R  R  R  R  t   exp(	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2009   s    c	   	         s     j  d  t t t  | | | | | |  | t d  |  | | | | t t | | t | | | | | |  |   t | |  | t d    t | |  | t d   t | | |  |  | | |  | |  S(   Ni  i   i   (	   R  R  R  t   PiR  R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2010   s    c	   	         s     j  d  t t t  | | | | | |  | t d  |  | | | | t t | | t | | | | | |  |   t | |  | t d    t | |  | t d   t | | |  |  | | |  | |  S(   Ni  i   i   (	   R  R  R  R  R  R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2011   s    c
   
         s     j  d  t t d  | |  | | t d  t | | t | | |	 | | |  |  | t d  |  |  t | | t | | |	 | | |  |  | t d  |	 | | | | |  | | t d  |  S(   Ni  i   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2012   s    c
   
         s     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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2013   s    t   ht   gc            s_     j  d  t t t | | t | | |
 | | |  |	  |   | | |  |	 |  S(   Ni  (   R  R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2014   s    R  c      	      sl     j  d  t | | t | | | | | |  |
  | t d  | |	 |  |
 | t d  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2015   s    t   mc            s     j  d  t | | |  | | t d  t | | 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  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2016   s    c            sR     j  d  t | | |  t d  t | | | | |   | | |  |  S(   Ni  i(   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2017   s    c      	      s     j  d  t | | | |  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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2018   s    c            s     j  d  t | | | | | |  |
 | t d  |  |
 | |	 | | t d  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  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2019   s    c            s*    j  d  t t t  | | | | | |  |
 | t d  |  |
 | |	 | | t d  t t | | t | | | | | |  |
   t | t d  | |  |
 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  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2020   s    c            s,    j  d  t t t  | | | | | |  |
 | t d  |  |
 | |	 | | t d  t t | | t | | | | | |  |
   t | t d  | |  |
 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  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2021   s    c            s    j  d  t | t d  | |  | | t d  t | | t | | | | |	 |  |  | t 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  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2022   s    c            sj    j  d  t | | | | |	 |  | | t d  |  | | | t | | | | |	 |  |  | t d  | |  | | | | t | | | | |	 |  |  | | |
 |	 | t 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  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2023   s    c            sI     j  d  t t t d  | | | t | |  |   | |  S(   Ni  i   (   R  R  R  R  R   (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2024   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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2025   s    c            s    j  d  t | | | |  |
 |	 t | | t | | | | | |  |
  | 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  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2026   s    c      
      s     j  d  t | | |  |
 |	 | t d  t | |	 | | t d  | | | |  |  t | | t | | | | | |  |
  | |	 | | t d  |	 | t d  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2027   s    i   c            s     j  d  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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2028   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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2029  s    c            sY     j  d  t t | |	 | | | | t | | | | | |  |
  |  |  S(   Ni  (   R  R   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2030  s    c            s    j  d  t | t d  | |  | | t d  t | | t | | | | |	 |  |  | t 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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2031  s    c      
      s]     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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2032  s    c      	      sV     j  d  t | | t | | t |  |	  | |
  | t | |	  | |	  S(   Ni  (   R  R   R  R1  (   t   vR  t   uR  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2033  s    c      	      sT     j  d  t | | t | | | | |	 |  |  | | |
 |	 | |	  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2034  s    t   jt   ic      	      s^     j  d  t | t t d  | | |  | |  | | |  | | |  | | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2035   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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2036%  s    c      
      s   t  | | |
 | | | |
 |
  }   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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2037)  s    'c      
      s     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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement20380  s    c      	   S   s   t  | t t t t f  r t St | | t |	 | | | | |  |  |
 | | | | | | | |  } t |  r t	 St S(   N(
   t
   isinstancet   intR  t   floatR  t   FalseR   R  R(   t   True(   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With20394  s    Tc      	      sn   t  | | t |	 | | | | |  |  |
 | | | | | | | |  }   j d  t | |  S(   Ni  (   R   R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2039<  s    Tc      	      s`     j  d  t | | t |	 | | | | |  |  |
 | | | | | | | |  S(   Ni  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2040C  s    c            sU     j  d  t |  t t d  | |  | | |  |  t d  | | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2041H  s    c      
      s     j  d  t | t t t d  | | |  |  | | | t d  |  |  t | | 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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2042M  s    c            sp     j  d  t | | t | | t | | | | | |  |
  | | | | | | | | |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2043R  s    c            sp     j  d  t |
 | t | | t | | |
 | | |  |	  |
 | | |
 | | | | |  |  S(   Ni  (   R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2044W  s    c            s   t  t d  t | | | t d   |  }   j d  t | | |  |	 t t | |
 | | |  |  |  t | | | t | | |
 | | |  |	  |  S(   Ni   i   i  (	   R  R  R  R  R  R   R,  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2045[  s    1c            s   t  t d  t |
 | | | |	 t d   |	  }   j d  t | | |  | t t | | | |	 |	  |	  |	  t | | | t | | | | |	 |  |  |	  S(   Ni   i   i  (	   R  R  R  R  R  R   R,  R  R  (   R  R  R  R  t   h1R  R  t   h2R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2046a  s    9R  R  c            s     j  d  t t t d  | | t d  |  t | | | t d   t | | 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  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2047h  s    c            s     j  d  t t t d  | | |	 t d  |
 |  t |
 | |	  t | | |	  t | | 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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2048m  s    t   kc            s    j  d  t | | |
 |  | | t | | t |	 | | | | |  |  |
 t d  t t d  t | | | | t d    | | | |  |  t | | t |	 | | | | |  |  |
 t t d  t | | | | t d    | |  S(   Ni  ii   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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2049r  s    c            s    j  d  t | | | |  | | | t |	 | t |
 | | | | |  |  | t d  t t d  | | | | |  | | | |  |  t |	 | t |
 | | | | |  |  | t t d  | | | | |  | | |  S(   Ni  ii   (   R  R  R   R  R  R  R  (   R  R  R	  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2050w  s    c            s    j  d  t | | | |  | | | t |
 | t | |	 | | | |  |  | t d  t | t d  | | | | |  | | | |  |  t |
 | t | |	 | | | |  |  | t | t d  | | | | |  | | |  S(   Ni  ii   (   R  R  R   R  R  R  R  (   R  R  R	  R  R  R  R  t   rR  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2051|  s    c      
      s   t  | | | |
 |	  | |	  }   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  t   FR  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2052  s    %R!  c            sn     j  d  t t d  | t t | | t | | |
 | | |  |	  | | |  | | |  |  S(   Ni  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2053  s    R  c            sn     j  d  t t d  | t t | | t | | | | |	 |  |
  | |	 |	  |	 |	 |  |	  S(   Ni  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2054  s    t   r1c            sj     j  d  t t d  | t t | | t | | | | |	 |  |
  | |	  |	 |	 |  |	  S(   Ni  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2055  s    c            sz     j  d  t t d  | t t | | t |	 | | | | |  |  |
 | | | | |  | | |  |  S(   Ni  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2056  s    c            s   t  t d  | | | t d  |  }   j d  t |  | t | | |  |  t | |  t | | |  | |  S(   Ni   i   i	  (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2057  s    +c      	      sY     j  d  t t t d  t | | | | | | | | |   | | |  S(   Ni
  i   (   R  R  R  R  R   (   R&  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2058  s    c      	      sY     j  d  t t t d  t | | | | | | | | |   | | |  S(   Ni  i   (   R  R  R  R  R   (   R&  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2059  s    c            sQ     j  d  t t | | | t | | |
 | | |  |	  | |  |  S(   Ni  (   R  R   R   R  (   R  R  R  R!  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2060  s    c      	   S   so   t  | t t t t f  r t St | | t | | |
 | | |  |	  | | |  } t |  rk 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  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2061  s    <c      	      sV   t  | | t | | |
 | | |  |	  | | |  }   j d  t | |  S(   Ni  (   R   R  R  R   (   R  R(  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2061  s    <c      
   S   sp   t  | t t t t f  r t St | | | t | | |
 | | |  |	  | |  } t |  rl 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  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2062  s    =c      
      sW   t  | | | t | | |
 | | |  |	  | |  }   j d  t | |  S(   Ni  (   R   R  R  R   (   R  R(  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2062  s    =R  c      
      st     j  d  t | | | t | t d  |  | | |  | 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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2063  s    c
   
   
      sI     j  d  t | | | t | | t |  |  | |	  | |  S(   Ni  (   R  R   R  R1  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2064  s    c            s`     j  d  t t t | | |  |  | |  | | |  | | | | | | |  |  S(   Ni  (   R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2065  s    c	   	         sh     j  d  t t | | t | | |  |  | |  | | |  | | | | | | |  |  S(   Ni  (   R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2066  s    R  c
   
         s@     j  d  t t |	 | | | |  |  t | |  |  S(   Ni  (   R  R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2067  s    R  c      	      s     j  d  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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2068  s    c            sH     j  d  t t t d  t | | |  | | |  | |  S(   Ni  i   (   R  R  R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2069  s    c      
      s*    j  d  t |	 | |  | | | | | t t | |
 | | | | | | | | |	  |  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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2070  s    c      
      s,    j  d  t |	 | |  | | | | | t t | |
 | | | | | | | | |	  |  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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2071  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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2072  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  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2073  s    c            si     j  d  t | t d  t | | | | | | |  | | t d  | | | | |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2074  s    c      	      s     j  d  t | t d  | |	 | | |
 |  | | |
 | | t d  | |  | | |
 t t | |	 | | |
 |  | | |
 |  |  | |   | t d  | |  | | |
 | | | | |
  S(   Ni  i   i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2075  s    c      	      s     j  d  t | t d  | |	 | | |
 |  | | |
 | | t d  | |  | | |
 t t | |	 | | |
 |  | | |
 |  |  | |   | t d  | |  | | |
 | | | | |
  S(   Ni  i   i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2076  s    c      	      s    j  d  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  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2077  s    c      	      s    j  d  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  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2078  s    i   c            s     j  d  t | | | | | t 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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2079  s    c            s     j  d  t | | | | | t 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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2080!  s    c      
      s-    j  d  t |
 | |  | | | |	 | | t d  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  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2081&  s    t   m2c            s     j  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  R  (   R  R  R0  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2082+  s    c	   	         s     j  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  R  (	   R  R  R0  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement20830  s    c
   
         s     j  d  t |	 |  | | t d  | | | | | t d  | | | | t d  t | t d  t |	 |  |  |  | | | | | |  S(   Ni$  i   i(   R  R  R  R  R  (
   R  R0  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement20845  s    c            s     j  d  t |  | t d  | | | | t d  | | | | t d  t | t d  t |    | | | | |  S(   Ni%  ii   (   R  R  R  R  R  (   R  R0  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2085:  s    c            s    j  d  t | t d  | |  t d  t | | |	 | | | |	 | t d  t |
 | |  |  t d  |	  |	  t | | |	 | t d  | | |	 | t d  t |
 | |  |  t d  | |  t d  | | | | |	  S(   Ni&  i   ii(   R  R  R  R   R  R  (   R  R  R0  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2086?  s    c	   	         s     j  d  t | t d  |  t d  t | | | | | | | | t d  t |  |  t d  |  |  t | | | | t d  | | | | t d  t |  |  t d  |  t d  | | | | |  S(   Ni'  i   ii(   R  R  R  R   R  R  (	   R  R  R0  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2087D  s    c      	      ss     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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2088I  s    c            s_     j  d  t t t d  |  | | | | | |  | | |  | | | |  |  S(   Ni)  i   (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2089N  s    c      
      sv    j  d  t |	 | |  | | | | | | | | t t | |
 | | | | | | | | |	  |  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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2090S  s    c      	      sd     j  d  t | t t d  | | | | | | | | | |  t d  | | |  S(   Ni+  i   (   R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2091X  s    c      	      s     j  d  t | t d  t t | |
 | | | | | | | | |	  |  | | | | | | | | | | |  |  S(   Ni,  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2092]  s    c      	      s     j  d  t | t d  | t t | |	 | | |
 | | | |
 | |  |  | | |
 | | |
 |
  |
  S(   Ni-  i   (   R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2093b  s    c            s     j  d  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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2094g  s    c
   
   	      s     j  d  t | | t t t d  t |  t d    t |	 | |  | t d  | | | | | | |  |  t t t d  t |  t d    t |	 | |  | | | | | |  S(   Ni/  i   i   i(   R  R  R   R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2095l  s    c      	      s     j  d  t | t t t d  t |  t d    t |  | t d  | | | | | | |  |  t t t d  t |  t d    t |  | | | | | |  S(   Ni0  i   i   i(   R  R  R   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2096q  s    c
            s   |  t  d  | }
   j d  t |
 | | t  d  t t |	 | |  | t  d  | | | | |
 | |
 | | |  |  t t |   t |	 | |  | t  d  | | t  d  | | | | |  S(   Ni   i1  (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2097u  s    c   	         s   |  t  d  | }   j d  t | | t  d  t t |  | t  d  | | | | | | | | | |  |  t t |  | t  d  t |   | t  d  | | | | |  S(   Ni   i2  (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2098{  s    c
   
   	      s     j  d  t | | t t t d  t |  t d    t |	 | |  | t d  | | | | | | |  |  t t t d  t |  t d    t |	 | |  | | | | | |  S(   Ni3  i   i   i(   R  R  R   R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2099  s    c      	      s     j  d  t | t t t d  t |  t d    t |  | t d  | | | | | | |  |  t t t d  t |  t d    t |  | | | | | |  S(   Ni4  i   i   i(   R  R  R   R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2100  s    c
            s   | |  t  d  }
   j d  t |
 | | t  d  t t |	 | |  | t  d  | | | | | | |
 | |
 |  |  t t |   t |	 | |  | t  d  | | t  d  | | | | |  S(   Ni   i5  (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2101  s    c   	         s   | |  t  d  }   j d  t | | t  d  t t |  | t  d  | | | | | | | | | |  |  t t |  | t  d  t |   | t  d  | | | | |  S(   Ni   i6  (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2102  s    c            s     j  d  t | | t t |	 t d  |   t |
 | |  | t d  | | | | | | |  |  t t |	 t d  |   t |
 | |  | | | | | |  S(   Ni7  i   i(   R  R  R   R  R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2103  s    c	   	         s     j  d  t | t t | t d  |   t |  | t d  | | | | | | |  |  t t | t d  |   t |  | | | | | |  S(   Ni8  i   i(   R  R  R   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2104  s    c            s     j  d  t t d  | | t d  t t |	 t d  |   t |
 | |  | t d  | | | | | | |  |  t t |	 |   t |
 | |  | t d  | | t d  | | | | |  S(   Ni9  i   i(   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2105  s    c	   	         s     j  d  t t d  | t d  t t | t d  |   t |  | t d  | | | | | | |  |  t 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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2106  s    c            s     j  d  t | | 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  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2107  s    c	   	         s     j  d  t | 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  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2108  s    c            s     j  d  t t d  | | t d  t t |	 t d  |   t |
 | |  | t d  | | | | | | |  |  t 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  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2109  s    c	   	         s     j  d  t t d  | t d  t t | t d  |   t |  | t d  | | | | | | |  |  t 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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2110  s    c      
      s}     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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2111  s    c      
      s}     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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2112  s    c      	      s   t  t d  | | |
 | |
 t d  |
  }   j d  t | | | | | t | | | |
 | | |
 |
  |
  t | t | |	 | | |
 |  | | |
 | |  |
  S(   Ni   i   iA  (   R  R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2113  s    3c      	      s   t  t d  | |
 |	 t d  |	  }   j d  t | | | | | t | | | |	 | | |	 |	  |	  t | t | | | | |	 |  | | |	 | |  |	  S(   Ni   i   iB  (   R  R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2114  s    +c         S   sw   t  |
 t t t t f  r t St t | |	 | | |
 | | | |
 | |  |  | |
  } t |  rs 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  R  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2115  s    Dc            s^   t  t | |	 | | |
 | | | |
 | |  |  | |
  }   j d  t | |
  S(   NiC  (   R   R  R  R   (   R  R(  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2115  s    Dc         S   sf   t  | t t t t f  r t St |  |  } t t t	 |  t
 t | t d      rb t St S(   Ni   (   R  R  R  R  R  R  R   R5   R  R  R   R  R  R  (   R  R  R  R  t   lst(    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2116  s    0c      	      s   t  |  |  }   j d  t | t | t | t d   t | t d   | t | t d   t | t d    | |  S(   NiD  i   i   i   i   (   R   R  R   R  R  R  (   R  R  R  R  RT  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2116  s    c      	      sn     j  d  t | | |  t | | | | | | |  |  t | t | | | | | |   |  S(   NiE  (   R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2117  s    c            s1     j  d  t t | t |  |  |  |  S(   NiF  (   R  R   R  R1  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2118  s    c
   
   
      s     j  d  t | |	 | |  | t | | t d  t | | |  | |	 | | |  |  t | | t | | |	 | | |   t | | |  | |  S(   NiG  i(   R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2119  s    c      
      s     j  d  t | |
 | |  | | t d  t |	 | t d  | | |	 | t d  | |
 |	 | |	  |	  t | | t | | |
 |	 | |   | | |	 | t d  | | t d  |	  S(   NiH  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2120  s    c            sJ     j  d  t | | t | t |  |  |  t | |  | |  S(   NiI  (   R  R   R  R1  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2121  s    c      
      s   t  t | | |	  | |	  }   j d  t | |
 | |  t t | |	 | t d  | |
 |	 | |	  |	  |	  t | | t | | |
 |	 | |   | |	  S(   NiJ  i(   R  R  R  R  R   R,  R  R  (   R  R  R  R  R  R  R  R  R  R  R  t   w(   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2122
  s    !c	   
         s   t  t d  | | | t d  |  }	   j d  t t d  | | |  t |	 | | | | t d  |  |  t |	 | | t | | | | t d  |   |  S(   Ni   i   iK  (   R  R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2123  s    +c            s     j  d  t t d  | | | |  t | t d  | | t | | | | t d  |   | t d  | | | t d  |  |  t | | | t | | | | t d  |   | |  S(   NiL  i   i(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2124  s    c	   	         s     j  d  t t d  d t t | | t d  t d  d | | t | | | | |   | |  | | t d   |  S(   NiM  i   i   i(   R  R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2125  s    c	   	         s    j  d  t t d  | | | |  | t d  t | | t d  | | t | | | | t d  |   | t d  | | | t d  |  |  t | | t d  | | t | | | | t d  |   | | t d  |  S(   NiN  i   i   i(   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2126!  s    c         S   s   t  | t t t t f  r t Sy7 t |  | |  t d  |  } t t	 |   } Wn t
 t f k
 rp t SX| r{ t St S(   Ni   (   R  R  R  R  R  R  R  R  R5   R   t	   TypeErrort   AttributeErrorR  (   R  R  R  R\  t   res(    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2127%  s    !c            s_   t  |  | |  t d  |  }   j d  t | t t d  t |  t d    |  S(   Ni   iO  i   (   R  R  R  R  R  R   (   R  R  R  R\  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement21271  s    !c         S   s   t  | t t t t f  r t Sy7 t |  | |  t d  |  } t t	 |   } Wn t
 t f k
 rp t SX| r{ t St S(   Ni   (   R  R  R  R  R  R  R  R  R5   R   Rb  Rc  R  (   R  R\  R  R  R  R  t   zRd  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With21287  s    !c            s   t  |  | |  t d  |  }   j d  t | t t | t | |  t t d  t |  t d    | |  |  |  t	 | | | t
 |  t t d  t |  t d    |  S(   Ni   iP  i   (   R  R  R  R  R   R,  R  R  R   R  R  (   R  R\  R  R  R  R  Rg  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2128C  s    !c      
      s     j  d  t | | |  t t d  | | | | | | |  |  t | | | t | | | | | | | |   | |  S(   NiQ  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2129J  s    c      
      s     j  d  t | | |  t t d  | | | | | | |  |  t | | | t | | | | | | | |   | |  t | |  | |  S(   NiR  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2130O  s    c
   
         s     j  d  t | |	 | |  | | t t | | t | | |	 | |   | t d  | |  | t d  | | |  |  t | | t | | |	 | | | |   | | | | | |	 | | |  S(   NiS  ii   (   R  R  R*   R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2131T  s    c      
      s     j  d  t | | |  t t | | | t | |  |  | t d  t | |  | |  |  |  t | | | t | |  |  | |  S(   NiT  i(   R  R  R   R,  R  R  R  R  (   R  R(  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2132Y  s    c	   	         s     j  d  t | | |  | t | | t | |  |  | t d  t | |  t | | |  | |  |  t | | t | |  |  | t | | |  | |  S(   NiU  i(   R  R  R   R  R  R  R  (	   R  R(  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2133^  s    c
   
   	      s     j  d  t | | |  |	 | t d  t t | | t | |  |  | t d  | |	 | | 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  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2134c  s    c            s   t  t d  | | | t d  |  }   j d  t | t t | t |  |  |  |  |  |  t | t |  | |  |  S(   Ni   i   iW  (	   R  R  R  R  R   R,  R  R  R  (   R(  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2135g  s    +c            sy   t  t d  | |  }   j d  t | t t | t |  |  |  |  |  |  t | t |  | |  |  S(   Ni   iX  (	   R  R  R  R  R   R,  R  R  R  (   R!  R  R  R$  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2136m  s    c   	      S   s_   t  | t t t t f  r t St | | t | |  |  | | |  } t |  r[ t	 St S(   N(
   R  R  R  R  R  R  R   R  R(   R  (	   R  R(  R  R  R  R  R)  R  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2137s  s    ,c   	         sF   t  | | t | |  |  | | |  }   j d  t | |  S(   NiY  (   R   R  R  R   (	   R  R(  R  R  R  R  R)  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2137{  s    ,c   	      S   s`   t  | t t t t f  r t St | | | t | |  |  | |  } t |  r\ t	 St S(   N(
   R  R  R  R  R  R  R   R  R(   R  (	   R  R(  R  R  R  R  R)  R  R  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2138  s    -c   	         sG   t  | | | t | |  |  | |  }   j d  t | |  S(   NiZ  (   R   R  R  R   (	   R  R(  R  R  R  R  R)  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2138  s    -c         S   s   t  | t t t t f  r t Sy7 t |  | | t |  |  } t t	 |   } Wn t
 t f k
 rp t SX| r{ t St S(   N(   R  R  R  R  R  R  RN  R  R5   R   Rb  Rc  R  (   R(  R  R  R  R  RT  Rd  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2139  s    !c            s   t  |  | | 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  R  R  RT  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2139  s    !c
   
         s     j  d  t | |  | | | t |  t | | | |  t d  t t d  |	 | | | | | |  |  |  t | | | |  t t d  |	 | | | | | |  | | | t |  |  S(   Ni\  ii   (   R  R  R  R   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2140  s    c            s    j  d  t | | | |  t t d  |
 |	 | | | | | |  |  t | | | |  t d  t t d  |
 |	 | | | | | |  | |  t d  |  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  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2141  s    c            sH    j  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 | t | | | |  t | | | | | t d    |  S(   Ni^  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2142  s    c            s     j  d  t | | |  t d  t | | | | | | t d  |  t | | | t d   | | | | | |  |  t | t | | | |  t | | | t d    |  S(   Ni_  i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2143  s    c	   	         s    j  d  t | t d  t d  | | | t d  t d  | |  t d  t | | |  t d  | t | | | | | t d   t d  | | | | | | | t d  | | | | t d  t d  | | | | | | | t d  |  |  t | | |  t d  t | | | | t | | | | | t d    | |  t d  |  S(   Ni`  i   i   i   (   R  R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2144  s    c            s    j  d  t | | | t d  | |  t d  t | | |  t d  | | | | | t d  | t | | | t d   | | | | | |  |  t | | |  t d  t | | | | t | | | t d    | |  t d  |  S(   Nia  i   i   (   R  R  R  R   R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2145  s    R  c      	      sC     j  d  t |  t | | | | t t | |    |  S(   Nib  (   R  R   R  R  R1  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2146  s    c            sL     j  d  t t |  t | |   | |   |   t |  t |  |   S(   Nic  (   R  R   R,  R  R  R  (   R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2147  s    c      	      s     j  d  t t d  | t t t | |   t | | |   | |   |   |   t t |  t | | |   | |   S(   Nid  i   (   R  R  R  R   R,  R  R  R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2148  s    c            s     j  d  t t d  | | t d  t t | | | | t d  t |  |  |  |  |  |  t | | | | t d  t |   | | t d  |  S(   Nie  i   (   R  R  R  R   R,  R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2149  s    c            se   t  t d  | |   }   j d  t t | t | |   | |   |   t | t |  |   S(   Ni   if  (   R  R  R  R   R,  R  R  R  (   R  R$  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2150  s    c            s`     j  d  t t | | |  t d  |  t | |   |   |   t | | |  | |   S(   Nig  i(   R  R   R,  R  R  R  (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2151  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  R\  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2152  s    c            sY   t  |  |  }   j d  t t |  | |  t t | t | |  | |  |  S(   Nih  (   R  R  R  R  R   R,  R  (   R  R  R  R\  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2152  s    c            s     j  d  t t | t |  |  t |  |  |  |  t t | t | |  t |   | |  |  t | t |   t |  |  S(   Nii  (   R  R   R,  R  R  R  (   R  R\  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2153  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  R  Rg  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2154  s    c            s   t  | |  }   j d  t t |   t |  | |  t t | t |  |  t |  |  |  |  t t | t | |  t |   | |  |  S(   Nij  (   R  R  R  R  R   R,  R  (   R  R\  R  R  Rg  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2154  s    c      	      sp     j  d  t | |  t t d  t | | |  |  |  t | t | t | | |  |   |  S(   Nik  i   (   R  R  R   R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2155   s    c            sQ     j  d  t |  t | t | | |  |   t | | |  | |  S(   Nil  (   R  R  R  (   R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2156  s    c      	      s     j  d  t | |  | t d  t | | t | | |  |  |  t | | t d  t | t | | |  |   | t d  |  S(   Nim  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2157
  s    t   At   Bc            s     j  d  t |  | t t | | t | | |   |  |  t | | |  | | t t d  t | | t | | |   |  |  S(   Nin  i   (   R  R  R   R  R  R  (   R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2158  s    c            s(     j  d  t | | t |  |   S(   Nio  (   R  R   R  (   R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2159  s    c         S   sq   t  |  t t t t f  r t Sy) t | |  |   } t t |   } Wn t	 t
 f k
 rb t SX| rm t St S(   N(   R  R  R  R  R  R  Ry  R5   R   Rb  Rc  R  (   R  R  RT  Rd  (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   With2160  s    c      
      s   t  | |  |   }   j d  t t d  t | t d   t t t | t d   |   |  t t | t d     |   S(   Nip  i   i   i   (   Ry  R  R  R  R  R*   R   R  (   R  R  RT  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2160$  s    c            sT     j  d  t t |   t t |    t | |  |  t | t |   |  S(   Niq  (   R  R  R  R  R  R   (   R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement2161+  s    c            s<     j  d  t | | | | | t |   | | |  S(   Nir  (   R  R   R  (   R  R\  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement21620  s    c      
      sH     j  d  t | | | t | | |
 | | |  |	  | |  S(   Nis  (   R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   replacement21635  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  t   x_R  R  R   t   n_R  t   m_t   u_t   v_t   p_t   a_R   t   g_t   e_t   g1_t   g2_R  t   r_t   F_t   f_t   d_t   mn_t   Px_t   RFx_t   q_t   n2_R  t   w_t   Qx_t   RGx_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  t   pattern2006R  t   rule2006t   pattern2007R  t   rule2007t   pattern2008R  t   rule2008t   pattern2009R  t   rule2009t   pattern2010R  t   rule2010t   pattern2011R  t   rule2011t   pattern2012R  t   rule2012t   pattern2013R  t   rule2013t   pattern2014R  t   rule2014t   pattern2015R  t   rule2015t   pattern2016R  t   rule2016t   pattern2017R  t   rule2017t   pattern2018R  t   rule2018t   pattern2019R  t   rule2019t   pattern2020R  t   rule2020t   pattern2021R  t   rule2021t   pattern2022R  t   rule2022t   pattern2023R  t   rule2023t   pattern2024R  t   rule2024t   pattern2025R  t   rule2025t   pattern2026R  t   rule2026t   pattern2027R  t   rule2027t   pattern2028R  t   rule2028t   pattern2029R  t   rule2029t   pattern2030R  t   rule2030t   pattern2031R  t   rule2031t   pattern2032R  t   rule2032t   pattern2033R  t   rule2033t   pattern2034R  t   rule2034t   pattern2035R  t   rule2035t   pattern2036R  t   rule2036R  t   pattern2037t   rule2037t   pattern2038R  t   rule2038R  t   pattern2039R  t   rule2039t   pattern2040R  t   rule2040t   pattern2041R  t   rule2041t   pattern2042R   t   rule2042t   pattern2043R  t   rule2043t   pattern2044R  t   rule2044R  t   pattern2045t   rule2045R  t   pattern2046t   rule2046t   pattern2047R  t   rule2047t   pattern2048R  t   rule2048t   pattern2049R
  t   rule2049t   pattern2050R  t   rule2050t   pattern2051R  t   rule2051R  t   pattern2052t   rule2052t   pattern2053R  t   rule2053t   pattern2054R  t   rule2054t   pattern2055R  t   rule2055t   pattern2056R  t   rule2056R  t   pattern2057t   rule2057t   pattern2058R  t   rule2058t   pattern2059R  t   rule2059t   pattern2060R  t   rule2060R  t   pattern2061R  t   rule2061R  t   pattern2062R  t   rule2062t   pattern2063R  t   rule2063t   pattern2064R  t   rule2064t   pattern2065R  t   rule2065t   pattern2066R   t   rule2066t   pattern2067R!  t   rule2067t   pattern2068R"  t   rule2068t   pattern2069R#  t   rule2069t   pattern2070R$  t   rule2070t   pattern2071R%  t   rule2071t   pattern2072R&  t   rule2072t   pattern2073R'  t   rule2073t   pattern2074R(  t   rule2074t   pattern2075R)  t   rule2075t   pattern2076R*  t   rule2076t   pattern2077R+  t   rule2077t   pattern2078R,  t   rule2078t   pattern2079R-  t   rule2079t   pattern2080R.  t   rule2080t   pattern2081R/  t   rule2081t   pattern2082R1  t   rule2082t   pattern2083R2  t   rule2083t   pattern2084R3  t   rule2084t   pattern2085R4  t   rule2085t   pattern2086R5  t   rule2086t   pattern2087R6  t   rule2087t   pattern2088R7  t   rule2088t   pattern2089R8  t   rule2089t   pattern2090R9  t   rule2090t   pattern2091R:  t   rule2091t   pattern2092R;  t   rule2092t   pattern2093R<  t   rule2093t   pattern2094R=  t   rule2094t   pattern2095R>  t   rule2095t   pattern2096R?  t   rule2096R@  t   pattern2097t   rule2097RA  t   pattern2098t   rule2098t   pattern2099RB  t   rule2099t   pattern2100RC  t   rule2100RD  t   pattern2101t   rule2101RE  t   pattern2102t   rule2102t   pattern2103RF  t   rule2103t   pattern2104RG  t   rule2104t   pattern2105RH  t   rule2105t   pattern2106RI  t   rule2106t   pattern2107RJ  t   rule2107t   pattern2108RK  t   rule2108t   pattern2109RL  t   rule2109t   pattern2110RM  t   rule2110t   pattern2111RN  t   rule2111t   pattern2112RO  t   rule2112RP  t   pattern2113t   rule2113RQ  t   pattern2114t   rule2114RR  t   pattern2115RS  t   rule2115RU  t   pattern2116RV  t   rule2116t   pattern2117RW  t   rule2117t   pattern2118RX  t   rule2118t   pattern2119RY  t   rule2119t   pattern2120RZ  t   rule2120t   pattern2121R[  t   rule2121R]  t   pattern2122t   rule2122R^  t   pattern2123t   rule2123t   pattern2124R_  t   rule2124t   pattern2125R`  t   rule2125t   pattern2126Ra  t   rule2126Re  t   pattern2127Rf  t   rule2127Rh  t   pattern2128Ri  t   rule2128t   pattern2129Rj  t   rule2129t   pattern2130Rk  t   rule2130t   pattern2131Rl  t   rule2131t   pattern2132Rm  t   rule2132t   pattern2133Rn  t   rule2133t   pattern2134Ro  t   rule2134Rp  t   pattern2135t   rule2135Rq  t   pattern2136t   rule2136Rr  t   pattern2137Rs  t   rule2137Rt  t   pattern2138Ru  t   rule2138Rv  t   pattern2139Rw  t   rule2139t   pattern2140Rx  t   rule2140t   pattern2141Ry  t   rule2141t   pattern2142Rz  t   rule2142t   pattern2143R{  t   rule2143t   pattern2144R|  t   rule2144t   pattern2145R}  t   rule2145t   pattern2146R~  t   rule2146t   pattern2147R  t   rule2147t   pattern2148R  t   rule2148t   pattern2149R  t   rule2149R  t   pattern2150t   rule2150t   pattern2151R  t   rule2151R  t   pattern2152R  t   rule2152t   pattern2153R  t   rule2153R  t   pattern2154R  t   rule2154t   pattern2155R  t   rule2155t   pattern2156R  t   rule2156t   pattern2157R  t   rule2157t   pattern2158R  t   rule2158t   pattern2159R  t   rule2159R  t   pattern2160R  t   rule2160t   pattern2161R  t   rule2161t   pattern2162R  t   rule2162t   pattern2163R  t   rule2163(    (   R  sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt
   logarithms   s<      j 	  1  ! ! " +    (    + E 	 a [ # #  d     M		  # #   ! ! - - ! ! 9 M P G - P ] C  		S}M	(	axQ			WQg%<	++	8|;	!4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  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  R  R  t   A_t   B_t   C_R  t   G_t   H_R  t   b_t   c_R  R  R  R  t   h_t   i_t   j_t   k_t   l_R  R  R  R  R  t   t_R  R  t   s_R  R  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_R  t   e1_t   e2_t   f1_t   f2_R  R  t   n3_t   Pq_t   Pm_R  t   Qm_t   Qr_R  t   jn_R  t   non2_R  R  t   iit   Pqqt   Qt   RR  t   CR	  R  R  t	   _UseGammat	   ShowStepst   Nonet   StepCounterR  (    (    (    sD   lib/python2.7/site-packages/sympy/integrals/rubi/rules/logarithms.pyt   <module>   s>   "           1nj:R4|'	