
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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     i      sX  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 ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t} d	 t~ d   t| t} d
 t~ d   t} d t~ d   t} d t~ d   t|  | | | | |	 |
 | | | | | |  }y   f d   }z t |y |z  }{ ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t} d	 t~ d   t| t} d
 t~ d   t} d t~ d   t t|  | | | | |	 |
 | | | | | |  }|   f d   }} t || |}  }~ ty tz 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 | |  } ty tz 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|  | | | |	 |
 | |  }   f d   } t | |  } ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t t| t} d
 t~ d   t} d t~ d    t|  | | | |	 |
 | |  }   f d   } t | |  } ty tz 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|  | | | |	 |
 | | | 	 }   f d   } t | |  } ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t t| t} d
 t~ d   t} d t~ d   t} d t~ d   t|  | | | | |	 |
 | | | |  }   f d   } t | |  } ty tz 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} d
 t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |	 |
 | | | |  }   f d   } t | |  } ty tz 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|  | | | | | |	 |
 | | | |  }   f d   } t | |  }   f d   } ty tz 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|  | | | | | |	 |
 | | | | |  } t | |  } ty tz t t} d t~ d   t{ t t} d t~ d   t} d	 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t|  | | | | | | | | | |  }   f d   } t | |  } d   } ty tz t t} d t~ d   t{ t t} d t~ d   t} d	 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t|  | | | | | | | | | | |  } t | |  } ty tz 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} d
 t~ d   t} d t~ d   t} d t~ d   t|  | | | | |	 |
 | | | | |  }   f d   } t | |  } ty tz 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 t{ 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 | |  } ty tz 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} 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 | |  } ty tz 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} 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 | |  } ty tz t t| t} d t~ d   t} d  t~ d   t} d! t~ d   t} d" t~ d   t} d# t~ d   t| t} d
 t~ 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$   } t | |  } ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t} d	 t~ d   t|  | | | | | |$  }   f d%   } t | |  } ty tz t{ t t} d t~ d   t t|  | | |% | |&  }   f d&   } t | |  } ty tz t{ t t} d t~ d   t t|  | | |% | |  }   f d'   } t | |  } ty tz t{ t t} d t~ d   t t} d t~ d   t t|  | | | |' |(  }   f d(   } t | |  } ty tz t{ t t} d t~ d   t t} d t~ d   t t|  | | |) | | | |&  }   f d)   } t | |  } ty tz t{ t t} d t~ d   t t} d t~ d   t t|  | | |) | | | |  }   f d*   } t | |  } d+   } ty tz t{ t t} d t~ d   t t} d t~ d   t t|  | | | |) | | |  } t | |  } ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} d
 t~ d    t t| t} d
 t~ d    t} d	 t~ d   t|  | | | | | |	 |
 | | | |* |+ |,  }   f d,   } t | |  } ty tz t{ t| t} d t~ d   t} d t~ d   t} d t~ d   t| t} d t~ d   t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} d
 t~ d    t t| t} d
 t~ d    t} d	 t~ d   t|  | | | | | |	 |
 | | | | |- |+ |,  }   f d-   } t | |  } ty tz t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |.  }   f d.   } t | |  } ty tz t{ t| t} d
 t~ d   t} d t~ d   t~ d/  t} d t~ d   t} d t~ d   t|  | | | | | |/  }   f d0   } t | |  } ty tz t{ t| t} d
 t~ d   t} d t~ d   t~ d/  t} d t~ d   t} d t~ d   t|  | | | | | |0  }   f d1   } t | |  } ty tz t{ t| t} d
 t~ d   t} d t~ d   t t} d t~ d   t} d t~ d   t|  | | | | | |1 |2  }   f d2   } t | |  }   f d3   } ty tz t{ t| t} d
 t~ d   t} d t~ d   t t} d t~ d   t} d t~ d   t|  | | | | | |1 |3  } t | |  } ty tz t{ t| t} d
 t~ d   t} d t~ d   t t} d t~ d   t} d t~ d   t|  | | | | | | |4  }   f d4   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | |	 |
 | |5 |6  }   f d5   } t | |  } ty tz 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 t~ d   t|  | | | | | |	 |
 | |6 
 }   f d6   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | | | |7 	 }   f d7   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | | |8 |9 |: |;  }   f d8   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | | | |8 |9 |< |=  }   f d9   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | | |8 |> |: |?  }   f d:   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | | | |8 |> |< |@  }   f d;   } t | |  }   f d<   } ty tz 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 t~ d   t} d t~ d   t|  | | | | | |A |8 |9 |3 
 } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | |	 |
 | | |6 |8 |B | |C  }   f d=   } t | |  } ty tz 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 t~ d   t} d t~ d   t|  | | | | | |	 |
 | | |6  }   f d>   } t | |  } ty tz 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 t|  | | | | | |	 |
 |D |E |F  }   f d?   } t | |  } ty tz 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 t|  | | | | | |	 |
 |D | |  }   f d@   } t | |  } ty tz 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 t~ d   t t|  | | | | | |	 |
 |D |: |G | |  }   f dA   } t | |  } ty tz 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 t~ d   t|  | | | | | |	 |
 |D 	 }   f dB   }t | | }ty tz 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 t~ d   t t|  | | | | | |	 |
 |D | |  }  f dC   }t || }ty tz 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 t~ d   t|  | | | | | |	 |
 | |D 
 }  f dD   }t || }ty tz t{ t t t} d t~ d   t|  | | |H |I |J  }	  f dE   }
t |	|
 }ty tz t{ t| t} d
 t~ d   t} d t~ d   t t} d t~ d   t} d t~ d   t t|  | | | | | | |%  }  f dF   }t || }ty tz t{ t t} d t~ d   t} d t~ d   t} dG t~ d   t|  | | | |% |K |L  }  f dH   }t || }ty tz 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 t~ d   t| t} d  t~ d   t} d t~ d   t|  | | | | | |	 |
 |6 	 }  f dI   }t || }ty tz 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| t} d  t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |	 |
 | | | |M  }  f dJ   }t || }ty tz 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| t} d  t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |	 |
 | | | |N |O  }  f dK   }t || }ty tz 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| t} d  t~ d   t} d t~ d   t|  | | | | | |	 |
 | | |N |P  }  f dL   }t || }ty tz 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| t} d  t~ d   t} d t~ d   t t|  | | | | | |	 |
 | | |N |P | |  }  f dM   }t || } ty tz 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| t} d  t~ d   t} d t~ d   t| t} d! t~ d   t} d t~ d   t|  | | | | | |	 |
 | | |O  }!  f dN   }"t |!|" }#ty tz t{ t| t~ d/  t} d t~ d   t| t} d t~ d   t} d t~ d   t|  | | | | |Q  }$  f dO   }%t |$|% }&ty tz t{ t t|  | |R |S  }'  f dP   }(t |'|( })ty tz t{ t| 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|  | | | | | |	 |T  }*  f dQ   }+t |*|+ },ty tz t{ t| 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 t|  | | | | | |	 |T | |F 
 }-  f dR   }.t |-|. }/ty tz t{ t| 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|  | | | | | |	 |T  }0  f dS   }1t |0|1 }2ty tz t{ t| 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 t|  | | | | | |	 |T | | 
 }3  f dT   }4t |3|4 }5ty tz t{ t| 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|  | | | | | |	 |U  }6  f dU   }7t |6|7 }8ty tz t{ t| 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 t|  | | | | | |	 |U | |F 
 }9  f dV   }:t |9|: };ty tz t{ t| 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 t|  | | | | | |	 |U | | 
 }<  f dW   }=t |<|= }>ty tz t{ t| 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|  | | | | | |	 | |V 	 }?  f dX   }@t |?|@ }Aty tz t{ t t t} d t~ d   t|  | | |H |R |W  }B  f dY   }Ct |B|C }D  f dZ   }Ety tz t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t| t} d t~ d   t{ t t} d t~ d   t} d t~ d   t t|  | | | | | |	 |X | | |2  }Ft |F|E }Gd[   }Hty tz 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 t} d	 t~ d   t|  | |Z | | | | |	 |
 | | | |Y t |H  }I  f d\   }Jt |I|J }Kd]   }Lty tz 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 t} d	 t~ d   t|  | |Z | | | | |	 |
 | | | |Y t |L  }M  f d^   }Nt |M|N }Oty tz 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 t} d	 t~ d   t|  | |Z | | | | |	 |
 | | |[ |\  }P  f d_   }Qt |P|Q }Rty tz 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 t t|  | |Z | | | | |	 |
 | | |[ |2  }S  f d`   }Tt |S|T }Uty tz 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 t t|  | |Z | | | | |	 |
 | | | |[ |3  }V  f da   }Wt |V|W }Xty tz t t t} d  t~ d   t{ t t} d t~ d   t} d t~ d   t t t|  | |Z | | |	 | | |] |^ 
 }Y  f db   }Zt |Y|Z }[dc   }\ty tz t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} dd t~ d   t} de t~ d   t} df 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|  | |Z |` | | | | |	 |
 | | |a |b |c | |_ t |\  }]  f dg   }^t |]|^ }_ty tz t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} dd t~ d   t} de t~ d   t} df 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|  | |Z |` | | | | |	 |
 | | |a |b |c |d |:  }`  f dh   }at |`|a }bty tz t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} dd t~ d   t} de t~ d   t} df 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|  | |Z |` | | | | |	 |
 | | |a |b |c |e |\  }c  f di   }dt |c|d }ety tz t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} dd t~ d   t} de t~ d   t} df t~ d   t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t t t|  | |Z |` | | | | |	 |
 | | |a |b |c |e |2  }f  f dj   }gt |f|g }hty tz t t| t} d t~ d   t} d t~ d   t} d  t~ d   t t| t} dd t~ d   t} de t~ d   t} df t~ d   t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t t t|  | |Z |` | | | | |	 |
 | | |a |b |c | |e |3  }i  f dk   }jt |i|j }kty tz t t t} d  t~ d   t t t} df t~ d   t{ t t} d t~ d   t} d t~ d   t t t|  | |Z |` | | |	 | |c | |' |f  }l  f dl   }mt |l|m }nty tz 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| t} d	 t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |	 | | | 
 }o  f dm   }pt |o|p }qty tz t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t| t} d t~ d   t{ t| t} d
 t~ d   t} d t~ d   t} d t~ d   t} d t~ d   t| t} d	 t~ d   t} d t~ d   t} d t~ d   t|  | | | | | |	 | | | |  }r  f dn   }st |r|s }t  f do   }uty tz t| t} d t~ d   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|  | | | | |
 | |g |H |h |i  }vt |v|u }w  f dp   }xty tz t{ t t| t} d t~ d   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|  | | | | |
 | |g |H |h |i  }yt |y|x }z  f dq   }{ty tz t{ t t} d t~ d   t t| t} d t~ d   t} d t~ d   t} d t~ d   t{ t t} d t~ d   t{ t t} d t~ d   t} d t~ d   t|  | | | | |
 | | |  |g |H |h |i  }|t |||{ }}  f dr   }~ty tz t| 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|  | | | | | |j | | 	 }t ||~ }ty tz t t{ t t} d t~ d   t{ t t} d t~ d   t t|  | | | | | |k |l |m 	 }  f ds   }t || }ty tz 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| t} d t~ d   t} d t~ d   t|  | | | | | |	 | | |n 
 }  f dt   }t || }ty tz 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|  | | | | |	 | | |o 	 }  f du   }t || }ty tz t{ t| t} d t~ d   t} d
 t~ d   t} d	 t~ d   t} d t~ d   t t} d t~ d   t t| t~ d/  t| t} d t~ d   t} d t~ d   t|  | | | | | |	 | | |% |  }  f dv   }t || }ty tz t{ t| t} d t~ d   t} d
 t~ d   t} d	 t~ d   t} d t~ d   t t} d t~ d   t t t| t~ d/  t|  | | | | |	 | | |% | 
 }  f dw   }t || }ty tz t{ t| t~ dx  t} d t~ d   t} d t~ d   t| t~ d/  t|  | | | |p  }  f dy   }t || }ty tz t| t} d t~ d   t| t} d t~ d   t t|  t t|  |A | |q |r  }  f dz   }t || }ty tz 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|  | | | | | |	 | |s 	 }  f d{   }t || }ty tz 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 	 }  f d|   }t || }ty tz t{ t t} d t~ d   t t} dG t~ d   t|  | | | |3  }  f d}   }t || }  f d~   }ty tz t t|  |u  }t || }ty tz t{ t t} d t~ d   t{ t t} d t~ d   t t} dG t~ d   t|  | | | | |2 |v  }  f d   }t || }ty tz t{ t t} d t~ d   t t t} d t~ d   t t} dG t~ d   t|  | |Z | | | |2 |v  }  f d   }t || }ty tz t{ t t} d t~ d   t{ t t} d t~ d   t t} dG t~ d   t|  | | | | |3 |v  }  f d   }t || }ty tz t{ t t} d t~ d   t t t} d t~ d   t t} dG t~ d   t|  | |Z | | | |3 |v  }  f d   }t || }ty tz t{ t t t t} dG t~ d   t|  | |Z |w  }  f d   }t || }d   }ty tz t{ t t t t} d t~ d   t|  | | t |  }  f d   }t || }d   }ty tz t{ t t t} d	 t~ d   t t|  | | |% |x |) t |  }  f d   }t || }|{ |~ | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|K|O|R|U|X|[|_|b|e|h|k|n|q|t|w|z|}|||||||||||||||||||gi S(   Ni(x   t   cons31t   cons168t   cons515t   cons1098t   cons1099t   cons3t   cons7t   cons27t   cons48t   cons125t   cons208t   cons4t   cons94t   cons17t   cons18t   cons21t   cons1100t   cons128t   cons2t   cons244t   cons137t   cons552t   cons1101t   cons1102t   cons5t   cons380t   cons54t   cons1103t   cons1104t   cons1105t   cons209t   cons224t   cons796t   cons797t   cons50t   cons1106t   cons804t   cons1107t   cons812t   cons1108t   cons1109t   cons1110t   cons1111t   cons584t   cons1112t   cons1113t   cons479t   cons480t   cons1114t   cons196t   cons23t   cons1115t   cons53t   cons1116t   cons1117t   cons1118t   cons1119t   cons85t   cons1120t   cons356t   cons531t   cons1121t   cons1122t   cons535t   cons93t   cons1123t   cons1124t   cons176t   cons367t   cons166t   cons744t   cons68t   cons840t   cons1125t   cons1126t   cons1127t   cons25t   cons71t   cons1128t   cons1129t   cons1130t   cons818t   cons1131t   cons1132t   cons1133t   cons1134t   cons819t   cons1135t   cons1136t   cons1137t   cons1138t   cons148t   cons810t   cons811t   cons1139t   cons1140t   cons52t   cons800t   cons1141t   cons1142t   cons1143t   cons813t   cons1144t   cons226t   cons62t   cons1145t   cons1146t   cons1147t   cons1148t   cons1149t   cons1150t   cons1151t   cons463t   cons1152t   cons43t   cons448t   cons1153t   cons1154t   cons1155t   cons1017t   fi   t   ei    t   gt   bt   nt   dt   ct   mc
   
         s     j  d  t | |  | | | t |  t | | |	 | | | | | | | |  t d  |  |  t | | |	 | | | | | | | |  | | | t |  |  S(   Nim  i(   t   appendR  t   logR   R  R  (
   R  R  R  R  R  R  R  t   xt   FR  (   t   rubi(    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1901   s    c
   
         s     j  d  t | | | t |  | |  t d  t | | |	 | | | | | | | |  t d  |  |  t | | |	 | | | | | | | |  t d  | |  t d  |  S(   Nin  i   (   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1902   s    c            s[     j  d  t | | | |  | | t |  | | | | t |  |  | |  S(   Nio  (   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1903   s    c            s     j  d  t | | | | | | | |  t d  | |  t d  | |  t |  t d  | | | | | t |  |  t |  |  t d  |  S(   Nip  ii   (   R  R  R  R  R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1904   s    c      
      sy     j  d  t t d  | t t | | | |  | | |  | | t d  | |  | t | | |   |  S(   Niq  i   (   R  R  R  R*   R   R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1905   s    c            s     j  d  t | | | | | | | | t |  | t |   t d  | | | | | t |  | t |   | | | t |   t |  t d  | | | | | t |  |  | |  S(   Nir  ii   (   R  R  R  R$   R  R%   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1906   s    c
   
         s{     j  d  t | | | |	 | | | | |	 | | | | t | | | |	 | | | | | |  |  |  S(   Nis  (   R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1907   s    t   pc      
      sR     j  d  t t | | |	 | | | |
 | | | |	 | |  |	  |	  S(   Nit  (   R  R   R   (   R  R  R  R  R  R  R  R  t   aR  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1908   s    c            s     j  d  t | |  | | | | t |	  t | | | |  t d  t | |	 | |
 | | | | t d   |  |  t | | | |  t | |	 | |
 | | | | t d   | | | | t |	  |  S(   Niu  ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1909   s    c            s   t  | | |
 | | | |	 | |  |	  }   j d  t | | t | | | |	 | t d  |	  |	  t | | |	 | | |	  S(   Niv  i(   R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  R  t   u(   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1910   s    /R  c
   
         sL     j  d  t | | |	 | t |  |  | | t | |  | |  S(   Niw  (   R  R   R1  R+  (
   t   vR  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1911   s    c
         S   s  t  | |  }
 t d  } t t t |
  t t |
 t d   |   t |
 t d   | t |
 t d   |
 |  } t t t |
  t t |
 d  |   t |
 d  | t |
 d  |
 |  } t |
 | t	 | | | |	 | t
 |  |  | | |  | |  S(   Nt   zi   i   (   R+  R  R  R  RV   R   R  R  R  R   R1  (   R  R  R  R  R  R  R  R  R  R  t   uuR  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1912   s
    cQc            sJ     j  d  t | | |
 | | | |	 | |  | | |	 | |	  S(   Niy  (   R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1913   s    c            s     j  d  t | |  | | | | t |	  t | | | |  t d  t t d  | |	 | |
 | | | |  |  |  t | | | |  t t d  | |	 | |
 | | | |  | | | | t |	  |  S(   Niz  ii   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1914   s    c      
      s    j  d  t | | | | | | |  t d  t |
  t | | |
 | | | |	 | |  t d  | | |	 | t d  |	  |	  t | | |
 | | | |	 | |  t d  | | |	 | | | | | |  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1915   s    c            sb     j  d  t | | |
 | | | |	 | |  | | |	 | |
 | | | |	 | |	  S(   Ni|  (   R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1916   s    t   it   ht   jt   kt   qc      
      s     j  d  t |	 | | | | | | | | | | | | t |
 | | | | | | | |  | | | | | | | | | | |  |  S(   Ni}  (   R  R  R   (   R  R  R  R  R  R  R  R  R  t   GR  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1917   s    c            sD     j  d  t | | | |  | | |  | | t |  |  S(   Ni~  (   R  R  R  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1918   s    c            s8     j  d  t t | | t |  |  | |  |  S(   Ni  (   R  R   R   R1  (   R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1919   s    c            s7     j  d  t t | | t |  |  | |  |  S(   Ni  (   R  R   R   R1  (   R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1920   s    c            s     j  d  t | | |  | | t d  t | | t d   | t | | t d   t |  | t d   t |  |  S(   Ni  i   (   R  R  R  R2   R  (   R  t   wR  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1921   s    c            sI     j  d  t t | | t |  |  | t | |  | |  |  S(   Ni  (   R  R   R   R1  R+  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1922   s    c            sH     j  d  t t | | t |  |  | t | |  | |  |  S(   Ni  (   R  R   R   R1  R+  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1923  s    c   	   	   S   s  t  | |  } t d  } t t t |  t t | t d   |   t | t d   | t | t d   | |  } t t t |  t t | d  |   t | d  | t | d  | |  } t | | t	 t
 | | t |  |  | | |  |  | |  S(   NR  i   i   (   R+  R  R  R  RV   R   R  R  R  R   R   R1  (	   R  R  R  R  R  R  R  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1924  s
    cQc            s\     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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1925  s    c            sj     j  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1926  s    c            s@     j  d  t | | |  | | | |  | t |  |  S(   Ni  (   R  R  R  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1927  s    i   c            s     j  d  t | | t t  t | | | t |  t |  t d    t d  | t |  t |  t d   |  S(   Ni  i   (   R  R  R  t   PiR  R  R  R  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1928  s    c            s     j  d  t | | t t  t | | | t |  t |  t d    t d  | t |  t |  t d   |  S(   Ni  i   (   R  R  R  R  R  R  R  R  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1929"  s    c      	      s     j  d  t |  | t |  t | | |  | | | | | | | | |  |  t | | |  | | | | | | | | |  S(   Ni  (   R  R  R  R   R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1930'  s    c      
      s~   t  |  }   j d  t | | t t | | |  | | | | | t d  |  | | | | t d  |  |  S(   Ni  ii   (   R3   R  R  R*   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1931+  s    c            s     j  d  t | | |  | | | | t |  t d  | | | | t t d  | |  | | | | t |   | | |  S(   Ni  i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement19322  s    c
   
         si     j  d  t | | | | | | | | | | | |	 | | | | | | t |  |  S(   Ni  (   R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement19337  s    c	   	         sJ     j  d  t | | t | | | | | t |   |  | |  S(   Ni  (   R  R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1934<  s    c      
      sv     j  d  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1935A  s    c      	      s     j  d  t |  | t d  | | t |  t | | | | | | | | | | |  | |  |  t | | | | | | | | | | |  | t d  | | | t |  |  S(   Ni  i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1936F  s    c      	      s     j  d  t |  | t d  | | t |  t | | | | | | | | | | |  | |  |  t | | | | | | | | | | |  | t d  | | | t |  |  S(   Ni  i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1937K  s    c      	      s     j  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1938P  s    c      	      s     j  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1939U  s    c   	   
      s   t  |  }   j d  t | | t t | | | | | | | | |  t d  t d  |  | | | | t d  |  |  S(   Ni  i   i(   R3   R  R  R*   R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1940Y  s    c
   
   	      sk     j  d  t | | | |  |	 | | |  t | | | | | | | | | | |  |  |  S(   Ni  (   R  R  R   (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1941`  s    c
   
         s     j  d  t | | | | | | | t |  |  t d  | |	 | | |  t d  t |  t d  | | | | | | t |   | | |  S(   Ni  i   (   R  R  R  R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1942e  s    c	   	   
      sm    j  d  t | | | | | t | | | | | | t d  | | | |  t d  |  |  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 |  |  S(   Ni  i   ii(   R  R  R   R  R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1943j  s    c	   	   
      s    j  d  t t d  | | t d  t |  | t d  |  t d  t | | | | | | t d  | | | |  t d  |  |  t t d  | | | | | | t |  | t d  |  t d  t | | | | | | t d  | | | |  t d  |  |  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1944o  s    c
   
   	      s     j  d  t | | | t |  | |  t d  t | | | | | | | | | | | t d  |	 | | |  t d  |  |  t | | | | | | | |	 | | |  t d  | |  t d  |  S(   Ni  i   i(   R  R  R  R  R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1945t  s    c      
      s     j  d  t | |  t | | | | | | | | | |  |  t | |  | | |  t | | | | | | | | | | |  | |  |  S(   Ni  (   R  R  R   (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1946y  s    c	   	   	      s     j  d  t | | t |  | |  t d  t | | | | | | | | | |  t d  | | | t d  |  |  t | | | | | | | | | |  t d  | |  t d  |  S(   Ni  i   i   (   R  R  R  R  R   R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1947~  s    c	   	         s>     j  d  t | | | | | | | | |  | |  S(   Ni  (   R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1948  s    c            s8     j  d  t | t |  |  t | |  | |  S(   Ni  (   R  R   R1  (   R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1949  s    c            sD     j  d  t t | | | | | | | |  | | |  |  S(   Ni  (   R  R   R   (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1950  s    R  c            s3     j  d  t | | | t |  |  | |  S(   Ni  (   R  R   R+  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1951  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1952  s    c            sB     j  d  t |	 | | | |
 t | | | |  |  |  S(   Ni  (   R  R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1953  s    c            sd     j  d  t |	 | | | | | | | | | | | | |
 | | | | |  |  S(   Ni  (   R  R   (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1954  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1955  s    c      	      s     j  d  t | | | | | t |	  | |  t d  t |	 |
 | | | | | | | | | | |  t d  | | | t d  |  |  t |	 |
 | | | | | | | | | | |  t d  | |  t d  |  S(   Ni  i   i   (   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1956  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1957  s    c            st     j  d  t | | |  t d  t d  | t | |  t d  | | t d  t d  | |  |  S(   Ni  i   i   (   R  R  R  R   (   R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1958  s    c            s'     j  d  t | t |  |  |  S(   Ni  (   R  R   R1  (   R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1959  s    c            sT     j  d  t | | |  | | | t d  | t d  | t |  |  S(   Ni  i   (   R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1960  s    c      	      s     j  d  t | t d  |  t d  t d  | t |  t | | | | | | t d  | | | |  t d  |  |  t | | | | | | t d  | | | | |  t d  t d  | t |  |  S(   Ni  i   ii(   R  R  R  R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1961  s    c            s     j  d  t | | |  t d  t d  | t |  t d  | | t d  t |  t d  |  t d  | |  S(   Ni  i   i   (   R  R  R  R  R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1962  s    c      	      s     j  d  t t d  | t |  | t d  |  t d  t | | | | | | t d  | | | |  t d  |  |  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1963  s    c      	      s     j  d  t |  | t d  | | t d  | t | | |  | | | t d  |  |  t | | |  | | | t d  | t d  | t |  |  S(   Ni  i   (   R  R  R  R   R  R  (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1964  s    c      
      se    j  d  t | | t d  | | t d  | t | | | | | | t d  | | | |  t d  |  |  t | t d  |  t d  t d  | t |  t | | | | | | t d  | | | |  t d  |  |  t | | | | | | t d  | | | | |  t d  t d  | t |  |  S(   Ni  i   ii(   R  R  R  R   R  R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1965  s    c      
      ss    j  d  t t d  | t |  | t d  |  t d  t | | | | | | t d  | | | |  t d  |  |  t | | t d  | | t |  | t d  |  t d  t | | | | | | t d  | | | |  t d  |  |  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1966  s    c            sH     j  d  t | | | | | | t d  | | | |  |  S(   Ni  i   (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1967  s    c            s8     j  d  t | t |  |  t | |  | |  S(   Ni  (   R  R   R1  (   R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1968  s    c
            s   t  | |	 | | | | |  | | | |  }
   j d  t | t |
 | | t d  |  |  t | | |
 |  S(   Ni  i(   R  R  R  R   R  (   R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1969  s    3c         S   s}   t  | t t t t f  r t St | |	 t |  | | t |
   } t t	 |  t
 t |  t d    ry t St S(   Ni   (   t
   isinstancet   intR  t   floatR  t   FalseR  R  R  R&   RQ   R  R  t   True(   R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1970  s    ,*c      
      s   t  | |	 t |  | | t |
   }   j d  t | | | |	 | |  |	 t |  | | t |
  t t | t |  t d  | | | t |  | |  | |
 | | | | t |   |  S(   Ni  i(	   R  R  R  R  R3   R*   R   Rw   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1970  s    ,c         S   s}   t  | t t t t f  r t St | | t |
  | |	 t |   } t t	 |  t
 t |  t d    ry t St S(   Ni   (   R  R  R  R  R  R  R  R  R  R&   RP   R  R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1971  s    ,*c      
      s   t  | | t |
  | |	 t |   }   j d  t t |  | |	 t |  t t | t |  t d  |
 | | | | |  | | | t |  | | |  | | |	 |  | | t |   |  S(   Ni  i(	   R  R  R  R  R3   R*   R   R  Rw   (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1971  s    ,c            sZ     j  d  t | |  |	 | | |	 | |
 | | |
 | | | | | | |  S(   Ni  (   R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1972  s    c            s     j  d  t | |	 |  | | | | t | | |	 t |  | | t |
  t d  | |	 t |  | | t |
  |
 | | | | | |  | |	 t |  |  S(   Ni  i   (   R  R  R4   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1973  s    c            s     j  d  t | |	 |  | | |
 | | | | | | | t d  t t d  | t d  | |	 t |  | | t |
  t d  | |	 t |  | | t |
  |
 | | | | | |  | | |	 t |  |  S(   Ni  i   (   R  R  R  R4   R  (   R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1974  s    c
   
         sL     j  d  t | | t | |  | |	 t |  |  | | | |  S(   Ni  (   R  R   R1  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1975  s    c         S   sq   t  | t t t t f  r t St | | t |  | |  t |
  | | t |   } t |  rm t	 St S(   N(
   R  R  R  R  R  R  R  R  R&   R  (   t   tR  R  R  t   rR  R  R  R  R  t   HR  R  t   sR  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1976!  s    >R  R  R  c      
      s
  t  | | t |  | |  t |
  | | t |   }   j d  t | | | | | | | |
 | | |  | | |  t |  | | t |  t t | t |  t d  |	 | | t |  | |  | | | | | | t |   |  S(   Ni  i(	   R  R  R  R  R3   R*   R   Rw   R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1976)  s    >c      
      sl     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  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement19770  s    c            sv     j  d  t | | | | | | | |
 | |  |
 | |  | | | | | | | | | |	 | |  S(   Ni  (   R  R   (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement19785  s    c            s    j  d  t | | | | | |
 |  | | | | |	 t |	 | | t |  | |  t |
  | | t |  t d  | | t |  | |  t |
  | | t |  | | | | | | |  | | t |  | |  t |
  |  S(   Ni  i   (   R  R  R4   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1979:  s    c            sB    j  d  t | | | | | |
 |  | | | | | | | | | | | |	 | | | | | | | |	 t |	 | | t |  | |  t |
  | | t |  t d  | | t |  | |  t |
  | | t |  | | | | | | |  | | t |  | |  t |
  |  S(   Ni  i   (   R  R  R4   R  R  (   R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1980?  s    c            sa     j  d  t | |
 t | |	  | | t | |	  | | t |  |	  | | | |	  S(   Ni  (   R  R   R1  (   R  R  R  R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1981D  s    c	   	   	      s     j  d  t | | | | | t |  t | | t d  | | | | | | | | | |  |  |  t | | | | | | | | | |  t d  | | | |  t d  t |  |  S(   Ni  ii   (   R  R  R  R   R  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1982I  s    c
   
   
      s_    j  d  t | | | | |	 t |  t | | | t d  | |	 | | | | | | | |  |  |  t | | | |	 |  t d  t |  t | | t d  | |	 | | | | | | | |  t d  |  |  t | | | |	 | | | | | | | |  t d  | | |	 |  t d  t |  |  S(   Ni  ii   (   R  R  R  R   R  R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1983N  s    c
            s   t  t d  | | | t d  t d   }
   j 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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1984R  s    2c
            s   t  t d  | | | t d  t d   }
   j 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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1985X  s    2c            s  t  t d  | | | t d  t d   }   j 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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1986^  s    2c   	         s   t  t d  | |  | | | | | | |  }   j 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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1987d  s    5c            sH     j  d  t | |  | | t d  |  | | |  | | |  S(   Ni  i   (   R  R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1988k  s    c	   	   	      s^     j  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1989p  s    c      	      sV     j  d  t t | |  | | | | t d  | | | t d  |  |  S(   Ni  i   i   (   R  R   R   R  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1990u  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  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1991z  s    c
   
   	      sT     j  d  t t | | | |	 | | |  | | | | t d  |  |  S(   Ni  i   (   R  R   R   R  (
   R  R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1992  s    i   c      	      sl    j  d  t t t  t |  t d  t | t |   t | t |   |   t t d  t | t |   t | t |    t d  t | t |   |   t t t  t |  t d  t | t |   t | t |   |   t t d  t | t |   t | t |    t d  t | t |   |   S(   Ni  i   i   (   R  R  R  R  R  R  R  t   exp(   R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1993  s    c            s     j  d  t | t |  | t d  |  | t |   | |   |   t |  | t |   | t d  |   t |  | t |   | t d  | t d  |   S(   Ni  ii   (   R  R  R   R  R%  R  (   R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1994  s    c      
      st     j  d  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1995  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  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1996  s    c            sK     j  d  t | | |  | |  | | t | | |  | |  |  S(   Ni  (   R  R  R   (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1997  s    c            s[   t  | |   }   j d  t | t | |   t t t | |   |  |   |  |  |   S(   Ni  (   R  R  R  R  R*   R   R  (   R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With1998  s    c            sH     j  d  t | | |  | | t |  | |  | | | |  S(   Ni  (   R  R   R1  (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement1999  s    c	   	   
      s^     j  d  t | | |  | | | t t |  t |  | t |  |   | |  S(   Ni  (   R  R   R%  R1  R  (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2000  s    c            s     j  d  t | | |  | |  | | | | | | t |  | |  | | | t | | |  | | t |  | |  | | | |  |  S(   Ni  (   R  R  R1  R   (   R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2001  s    c	   	         s     j  d  t | | |  | | t t |  t |  | t |  |   | | |  | | | | | t | | |  | | | t t |  t |  | t |  |   | |  |  S(   Ni  (   R  R  R%  R1  R  R   (	   R  R  R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2002  s    c            sE     j  d  t | t t |  t |  | t |   |  |  S(   Ni  (   R  R   R"  R%  R  (   R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2003  s    c         S   sf   t  | t t t t f  r t S|  | t | |  t |  } t | | t | |   rb t	 St S(   N(
   R  R  R  R  R  R  R  R  R   R  (   R  R  R  t   yR  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With2004  s    !R1  c            sC   |  | t  | |  t |  }   j d  t | | | |  S(   Ni  (   R  R  R  R  (   R  R  R  R1  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2004  s    !c         S   s   t  | t t t t f  r t S|  t | |  t |  | t d  t |  |  } t	 t
 t | |  t | |   t | t | | t | |   | t | | t | |     r t St S(   Ni   (   R  R  R  R  R  R  R  R  R  R  R"   R   R   R2   R  (   R  R  R  R  R  R  R  (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   With2005  s    8fc            s   |  t  | |  t |  | t d  t  |  |  }   j d  t | | |  | t d  t | | t | |   t | | t | |   |  S(   Ni   i  (   R  R  R  R  R  R2   R   (   R  R  R  R  R  R  R  (   R  (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   replacement2005  s    8(   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  t   F_t   x_R  R  R   t   m_R  t   n_t   a_t   p_t   u_t   v_t   G_t   w_t   e_R  R   t   H_t   h_t   c_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  t   pattern1901R  t   rule1901t   pattern1902R  t   rule1902t   pattern1903R  t   rule1903t   pattern1904R  t   rule1904t   pattern1905R  t   rule1905t   pattern1906R  t   rule1906t   pattern1907R  t   rule1907t   pattern1908R  t   rule1908t   pattern1909R  t   rule1909R  t   pattern1910t   rule1910t   pattern1911R  t   rule1911R  t   pattern1912t   rule1912t   pattern1913R  t   rule1913t   pattern1914R  t   rule1914t   pattern1915R  t   rule1915t   pattern1916R  t   rule1916t   pattern1917R  t   rule1917t   pattern1918R  t   rule1918t   pattern1919R  t   rule1919t   pattern1920R  t   rule1920t   pattern1921R  t   rule1921t   pattern1922R  t   rule1922t   pattern1923R  t   rule1923R  t   pattern1924t   rule1924t   pattern1925R  t   rule1925t   pattern1926R  t   rule1926t   pattern1927R  t   rule1927t   pattern1928R  t   rule1928t   pattern1929R  t   rule1929t   pattern1930R  t   rule1930R  t   pattern1931t   rule1931t   pattern1932R  t   rule1932t   pattern1933R  t   rule1933t   pattern1934R  t   rule1934t   pattern1935R  t   rule1935t   pattern1936R  t   rule1936t   pattern1937R  t   rule1937t   pattern1938R  t   rule1938t   pattern1939R  t   rule1939R  t   pattern1940t   rule1940t   pattern1941R  t   rule1941t   pattern1942R  t   rule1942t   pattern1943R  t   rule1943t   pattern1944R  t   rule1944t   pattern1945R  t   rule1945t   pattern1946R  t   rule1946t   pattern1947R  t   rule1947t   pattern1948R  t   rule1948t   pattern1949R  t   rule1949t   pattern1950R  t   rule1950t   pattern1951R  t   rule1951t   pattern1952R  t   rule1952t   pattern1953R  t   rule1953t   pattern1954R  t   rule1954t   pattern1955R  t   rule1955t   pattern1956R  t   rule1956t   pattern1957R  t   rule1957t   pattern1958R  t   rule1958t   pattern1959R  t   rule1959t   pattern1960R  t   rule1960t   pattern1961R  t   rule1961t   pattern1962R  t   rule1962t   pattern1963R  t   rule1963t   pattern1964R  t   rule1964t   pattern1965R  t   rule1965t   pattern1966R  t   rule1966t   pattern1967R  t   rule1967t   pattern1968R   t   rule1968R  t   pattern1969t   rule1969R  t   pattern1970R  t   rule1970R	  t   pattern1971R
  t   rule1971t   pattern1972R  t   rule1972t   pattern1973R  t   rule1973t   pattern1974R  t   rule1974t   pattern1975R  t   rule1975R  t   pattern1976R  t   rule1976t   pattern1977R  t   rule1977t   pattern1978R  t   rule1978t   pattern1979R  t   rule1979t   pattern1980R  t   rule1980t   pattern1981R  t   rule1981t   pattern1982R  t   rule1982t   pattern1983R  t   rule1983R  t   pattern1984t   rule1984R  t   pattern1985t   rule1985R  t   pattern1986t   rule1986R  t   pattern1987t   rule1987t   pattern1988R   t   rule1988t   pattern1989R!  t   rule1989t   pattern1990R"  t   rule1990t   pattern1991R#  t   rule1991t   pattern1992R$  t   rule1992t   pattern1993R&  t   rule1993t   pattern1994R'  t   rule1994t   pattern1995R(  t   rule1995t   pattern1996R)  t   rule1996t   pattern1997R*  t   rule1997R+  t   pattern1998t   rule1998t   pattern1999R,  t   rule1999t   pattern2000R-  t   rule2000t   pattern2001R.  t   rule2001t   pattern2002R/  t   rule2002t   pattern2003R0  t   rule2003R2  t   pattern2004R3  t   rule2004R4  t   pattern2005R5  t   rule2005(    (   R  sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   exponential   s     	 / T T yw??V\\	\  "w~~~?d o"?		}	 8 / /   # gcYOpsps=	C	L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_R7  R?  RB  R;  t   b_RD  t   d_RA  t   f_t   g_RC  t   i_t   j_t   k_t   l_R9  R:  R<  t   q_t   r_t   t_R=  R>  t   s_R@  R8  t   y_t   z_t   a1_t   a2_t   b1_t   b2_t   c1_t   c2_t   d1_t   d2_t   n1_t   n2_t   e1_t   e2_t   f1_t   f2_t   g1_t   g2_t   n3_t   Pq_t   Pm_t   Px_t   Qm_t   Qr_t   Qx_t   jn_t   mn_t   non2_t   RFx_t   RGx_t   iit   Pqqt   Qt   RR  t   CR  R  R  t	   _UseGammat	   ShowStepst   Nonet   StepCounterR  (    (    (    sE   lib/python2.7/site-packages/sympy/integrals/rubi/rules/exponential.pyt   <module>   s>   "           1nj:R4|'	