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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 mĄZĄm˘Z˘mŁZŁm¤Z¤mĽZĽmŚZŚm§Z§m¨Z¨mŠZŠmŞZŞmŤZŤmŹZŹmJZJm­Z­mŽZŽmŻZŻm°Z°mąZąm˛Z˛młZłm´Z´mľZľmśZśmˇZˇm¸Z¸mšZšmşZşmťZťmźZźm˝Z˝mžZžmżZżmŔZŔmÁZÁmÂZÂmĂZĂmÄZÄmĹZĹmĆZĆmÇZÇmČZČmÉZÉmÂZÂmĘZĘmËZËmĚZĚmÍZÍmÎZÎmĎZĎmĐZĐmŃZŃmŇZŇmÓZÓmÔZÔmŐZŐmÖZÖm×Z×mŘZŘmŮZŮmÚZÚmŰZŰmÜZÜmÝZÝmŢZßmŕZámâZâmăZămäZäd d lĺmćZćmçZçmčZčméZémęZęmëZëměZěmíZímîZîmďZďmđZđmńZńmňZňmóZómôZômőZőd d löm÷Z÷d d	 lřmůZůmúZúd d
 lűmüZümýZýmţZţm˙Z˙m Z mZmčZč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 lĺmZg  d D] Ze÷e ^ qç\ 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eů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(Ú  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   FactorRž  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   secRá  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      Ŕ      snr  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] }] t^ t_ t` ta tb d tc d   tb d tc d    ta  | | |  }^   f d   }_ td |^ |_  }` t^ t_ te ta tb d tc d   tb d tc d    ta  | | |  }a   f d   }b td |a |b  }c t^ t_ tf ta tb d tc d   tb d tc d    ta  | | |  }d   f d	   }e td |d |e  }f t^ t_ t` ta tb d tc d    ta ta  | |  }g   f d
   }h td |g |h  }i t^ t_ te ta tb d tc d    ta ta  | |  }j   f d   }k td |j |k  }l t^ t_ tf ta tb d tc d    ta ta  | |  }m   f d   }n td |m |n  }o t^ t_ ta tb d tc d   t` ta tb d tc d   tb d tc d    ta  | | | |  }p   f d   }q td |p |q  }r t^ t_ ta tb d tc d   te ta tb d tc d   tb d tc d    ta  | | | |  }s   f d   }t td |s |t  }u t^ t_ ta tb d tc d   tf ta tb d tc d   tb d tc d    ta  | | | |  }v   f d   }w td |v |w  }x t^ t_ ta t` ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |  }y   f d   }z td |y |z  }{ t^ t_ ta te ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |  }|   f d   }} td || |}  }~ t^ t_ ta tf ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |  }   f d   } td | |  } t^ t_ ta th t` ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |
  }   f d   } td | |  } t^ t_ ta th te ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |
  }   f d   } td | |  } t^ t_ ta th tf ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |
  }   f d   } td | |  } t^ t_ t` ta tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta ta  | |  }   f d   } td | |  } t^ t_ te ta tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta ta  | |  }   f d   } td | |  } t^ t_ tf ta tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta ta  | |  }   f d   } td | |  } t^ t_ ta th t` ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |  }   f d   } td | |  } t^ t_ ta th te ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |  }   f d   } td | |  } t^ t_ ta th tf ta tb d tc d   tb d tc d    tg ta tc d  tb d tc d   tb d tc d    ta  | | | | |	 |  }   f d   } td | |  } t^ t_ t` ta tb d tc d   tb d tc d    tc d  ta  | | |  }   f d    } td | |  } t^ t_ te ta tb d tc d   tb d tc d    tc d  ta  | | |  }    f d!   }Ą td |  |Ą  }˘ t^ t_ tf ta tb d tc d   tb d tc d    tc d  ta  | | |  }Ł   f d"   }¤ td |Ł |¤  }Ľ t^ t_ ta tb d tc d   t` ta tb d tc d    tc d  ta  | |	 | |  }Ś   f d#   }§ td |Ś |§  }¨ t^ t_ ta tb d tc d   te ta tb d tc d    tc d  ta  | |	 | |  }Š   f d$   }Ş td |Š |Ş  }Ť t^ t_ ta tb d tc d   tf ta tb d tc d    tc d  ta  | |	 | |  }Ź   f d%   }­ td |Ź |­  }Ž t^ t_ ta tb d tc d   t` ti ta tb d tc d    tc d  ta  | | |  }Ż   f d&   }° td |Ż |°  }ą t^ t_ ta tb d tc d   te ti ta tb d tc d    tc d  ta  | | |  }˛   f d'   }ł td |˛ |ł  }´ t^ t_ ta tb d tc d   tf ti ta tb d tc d    tc d  ta  | | |  }ľ   f d(   }ś td |ľ |ś  }ˇ t^ t_ tj ta tb d tc d   tb d tc d    ta  | | |  }¸   f d)   }š td |¸ |š  }ş t^ t_ tk ta tb d tc d   tb d tc d    ta  | | |  }ť   f d*   }ź td |ť |ź  }˝ t^ t_ tj ta tb d tc d    ta ta  | |  }ž   f d+   }ż td |ž |ż  }Ŕ t^ t_ tk ta tb d tc d    ta ta  | |  }Á   f d,   }Â td |Á |Â  }Ă t^ t_ ta tb d tc d   tj ta tb d tc d   tb d tc d    ta  | | | |  }Ä   f d-   }Ĺ td |Ä |Ĺ  }Ć t^ t_ ta tb d tc d   tk ta tb d tc d   tb d tc d    ta  | | | |  }Ç   f d.   }Č td |Ç |Č  }É t^ t_ tj ta tb d tc d   tb d tc d    tc d  ta  | | |  }Ę   f d/   }Ë td |Ę |Ë  }Ě t^ t_ tk ta tb d tc d   tb d tc d    tc d  ta  | | |  }Í   f d0   }Î td |Í |Î  }Ď t^ t_ ta th tj ta tb d tc d    tc d  ta  | |	 | |  }Đ   f d1   }Ń td |Đ |Ń  }Ň t^ t_ ta th tk ta tb d tc d    tc d  ta  | |	 | |  }Ó   f d2   }Ô td |Ó |Ô  }Ő t^ t_ ta tj ta tb d tc d    tl ta tc d  tb d tc d    ta  | | |  }Ö   f d3   }× td |Ö |×  }Ř t^ t_ ta tk ta tb d tc d    tm ta tc d  tb d tc d    ta  | | |  }Ů   f d4   }Ú td |Ů |Ú  }Ű t^ t_ ta th tj ta tb d tc d    tl ta tc d  tb d tc d    ta  | | | |	 |
 |  }Ü   f d5   }Ý td |Ü |Ý  }Ţ t^ t_ ta th tk ta tb d tc d    tm ta tc d  tb d tc d    ta  | | | |	 |
 |  }ß   f d6   }ŕ td |ß |ŕ  }á t^ t_ ta th tj ta tb d tc d    tl ta tc d  tb d tc d    ta  | | | |	 | |  }â   f d7   }ă td |â |ă  }ä t^ t_ ta th tk ta tb d tc d    tm ta tc d  tb d tc d    ta  | | | |	 | |  }ĺ   f d8   }ć td |ĺ |ć  }ç t^ t_ ta tj ta tb d tc d    tm ta tc d  tb d tc d    ta  | | |  }č   f d9   }é td |č |é  }ę t^ t_ ta tk ta tb d tc d    tl ta tc d  tb d tc d    ta  | | |  }ë   f d:   }ě td |ë |ě  }í t^ t_ ta th tj ta tb d tc d    tm ta tc d  tb d tc d    ta  | | | |	 |
 |  }î   f d;   }ď td |î |ď  }đ t^ t_ ta th tk ta tb d tc d    tl ta tc d  tb d tc d    ta  | | | |	 |
 |  }ń   f d<   }ň td |ń |ň  }ó t^ t_ ta th tj ta tb d tc d    tm ta tc d  tb d tc d    ta  | | | |	 | |  }ô   f d=   }ő td |ô |ő  }ö t^ t_ ta th tk ta tb d tc d    tl ta tc d  tb d tc d    ta  | | | |	 | |  }÷   f d>   }ř td |÷ |ř  }ů t^ t_ tn to ta tb d tc d   tb d tc d    ta  | | | |  }ú   f d?   }ű td |ú |ű  }ü t^ t_ ta tb d tc d   tn to ta tb d tc d    ta  | | |  }ý   f d@   }ţ td |ý |ţ  }˙ t^ t_ tn tc d  ta tb d tc d    ta ta  | |  }   f dA   }td | | }t^ t_ ta th tn to ta tb d tc d    ta  | | |	 |  }  f dB   }td || }t^ t_ ta th tn to ta tb d tc d    ta  | | | | |  }  f dC   }td || }t^ t_ ta tb d tc d   tn to ta tb d tc d    ta  | | | |  }	  f dD   }
td |	|
 }t^ t_ ta tb d tc d   tn to ti ta tb d tc d    ta  | | | | |  }  f dE   }td || }t^ t_ ta tb d tc d   tn to ti ta tb d tc d    ta  | | | | |  }  f dF   }td || }t^ t_ tp ta tb d tc d   tb d tc d    ta  | | |  }  f dG   }td || }t^ t_ ta tb d tc d   tp ta tb d tc d   tb d tc d    ta  | | | |  }  f dH   }td || }t^ t_ tp ta tb d tc d   tb d tc d    tc d  ta  | | |  }  f dI   }td || }t^ t_ ta tb d tc d   tp ta tb d tc d    tc d  ta  | |  }  f dJ   }td || }t^ t_ ta tb d tc d   tp ti ta tb d tc d    tc d  ta  | | |  }  f dK   }td || } t^ t_ tp ta tb d tc d   tb d tc d    tg ta tb d tc d   tb d tc d    ta  | | | | |  }!  f dL   }"td |!|" }#t^ t_ ta tb d tc d   tp ta tb d tc d   tb d tc d    tg ta tb d tc d   tb d tc d    ta  | | | | |  }$  f dM   }%td |$|% }&t^ t_ ta th tp ta tb d tc d   tb d tc d    tg ta tb d tc d   tb d tc d    ta  | | | | |	 |  }'  f dN   }(td |'|( })t^ t_ tq ta tb d tc d   tb d tc d    ta  | | |  }*  f dO   }+td |*|+ },t^ t_ tq ta tb d tc d    ta ta  | |  }-  f dP   }.td |-|. }/t^ t_ ta tb d tc d   tq ta tb d tc d   tb d tc d    ta  | | | |  }0  f dQ   }1td |0|1 }2t^ t_ tr ta tb d tc d   tb d tc d    ta  | | |  }3  f dR   }4td |3|4 }5t^ t_ ts ta tb d tc d   tb d tc d    ta  | | |  }6  f dS   }7td |6|7 }8t^ t_ tr ta tb d tc d    ta ta  | |  }9  f dT   }:td |9|: };t^ t_ ts ta tb d tc d    ta ta  | |  }<  f dU   }=td |<|= }>t^ t_ ta tb d tc d   tr ta tb d tc d   tb d tc d    ta  | | | |  }?  f dV   }@td |?|@ }At^ t_ ta tb d tc d   ts ta tb d tc d   tb d tc d    ta  | | | |  }B  f dW   }Ctd |B|C }Dt^ t_ tr ta tb d tc d   tb d tc d    tc d  ta  | | |  }E  f dX   }Ftd |E|F }Gt^ t_ ts ta tb d tc d   tb d tc d    tc d  ta  | | |  }H  f dY   }Itd |H|I }Jt^ t_ ta tb d tc d   tr ta tb d tc d    tc d  ta  | |  }K  f dZ   }Ltd |K|L }Mt^ t_ ta tb d tc d   ts ta tb d tc d    tc d  ta  | |  }N  f d[   }Otd |N|O }Pt^ t_ ta tb d tc d   tr ti ta tb d tc d    tc d  ta  | | |  }Q  f d\   }Rtd |Q|R }St^ t_ ta tb d tc d   ts ti ta tb d tc d    tc d  ta  | | |  }T  f d]   }Utd |T|U }Vt^ t_ tr ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |  }W  f d^   }Xtd |W|X }Yt^ t_ ts ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |  }Z  f d_   }[td |Z|[ }\t^ t_ ta tb d tc d   tr ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |  }]  f d`   }^td |]|^ }_t^ t_ ta tb d tc d   ts ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |  }`  f da   }atd |`|a }bt^ t_ ta th tr ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |	 |  }c  f db   }dtd |c|d }et^ t_ ta tb d tc d   ts ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |	 |  }f  f dc   }gtd |f|g }ht^ t_ tr ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |  }i  f dd   }jtd |i|j }kt^ t_ ts ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |  }l  f de   }mtd |l|m }nt^ t_ ta tb d tc d   tr ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |  }o  f df   }ptd |o|p }qt^ t_ ta tb d tc d   ts ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |  }r  f dg   }std |r|s }tt^ t_ ta tb d tc d   tr ta tb d tc d   tb d tc d    tm ta tb d tc d   tb d tc d    ta  | | | | |	 |  }u  f dh   }vtd |u|v }wt^ t_ ta th ts ta tb d tc d   tb d tc d    tl ta tb d tc d   tb d tc d    ta  | | | | |	 |  }x  f di   }ytd |x|y }zt^ t_ tt ta tb d tc d   tb d tc d    ta  | | |  }{  f dj   }|td |{|| }}t^ t_ tu ta tb d tc d   tb d tc d    ta  | | |  }~  f dk   }td |~| }t^ t_ tt ta tb d tc d    ta ta  | |  }  f dl   }td || }t^ t_ tu ta tb d tc d    ta ta  | |  }  f dm   }td || }t^ t_ ta tb d tc d   tt ta tb d tc d   tb d tc d    ta  | | | |  }  f dn   }td || }t^ t_ ta tb d tc d   tu ta tb d tc d   tb d tc d    ta  | | | |  }  f do   }td || }t^ t_ tt ta tb d tc d   tb d tc d    tc d  ta  | | |  }  f dp   }td || }t^ t_ tu ta tb d tc d   tb d tc d    tc d  ta  | | |  }  f dq   }td || }t^ t_ ta tb d tc d   tt ta tb d tc d    tc d  ta  | |  }  f dr   }td || }t^ t_ ta tb d tc d   tu ta tb d tc d    tc d  ta  | |  }  f ds   }td || }t^ t_ ta tb d tc d   tt ti ta tb d tc d    tc d  ta  | | |  }  f dt   }td || }t^ t_ ta tb d tc d   tu ti ta tb d tc d    tc d  ta  | | |  }  f du   }td || }t^ t_ tt ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |  }  f dv   } td ||  }Ąt^ t_ tu ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |  }˘  f dw   }Łtd |˘|Ł }¤t^ t_ ta tb d tc d   tt ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |	 |   }Ľ  f dx   }Śtd |Ľ|Ś }§t^ t_ ta tb d tc d   tu ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |	 |   }¨  f dy   }Štd |¨|Š }Şt^ t_ ta th tt ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |	 |  }Ť  f dz   }Źtd |Ť|Ź }­t^ t_ ta tb d tc d   tu ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |	 |  }Ž  f d{   }Żtd |Ž|Ż }°t^ t_ tt ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |  }ą  f d|   }˛td |ą|˛ }łt^ t_ tu ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |  }´  f d}   }ľtd |´|ľ }śt^ t_ ta tb d tc d   tt ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |  }ˇ  f d~   }¸td |ˇ|¸ }št^ t_ ta tb d tc d   tu ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |  }ş  f d   }ťtd |ş|ť }źt^ t_ ta tb d tc d   tt ta tb d tc d   tb d tc d    tw ta tb d tc d   tb d tc d    ta  | | | | |	 |  }˝  f d   }žtd |˝|ž }żt^ t_ ta th tu ta tb d tc d   tb d tc d    tv ta tb d tc d   tb d tc d    ta  | | | | |	 |  }Ŕ  f d   }Átd |Ŕ|Á }Ât^ t_ tx to ta tb d tc d   tb d tc d    ta  | | |  }Ă  f d   }Ätd |Ă|Ä }Ĺt^ t_ tx to ty ta  ta ta  | | |!  }Ć  f d   }Çtd |Ć|Ç }Čt^ t_ ta tb d tc d   tx to ty ta  ta  | | | |  }É  f d   }Ętd |É|Ę }Ë  f d   }Ět^ t_ ta tb d tc d   tx to ti ta tb d tc d    ta  | | | | |" |  }Ítd |Í|Ě }Ît^ t_ tz ta tb d tc d   tb d tc d    ta  | | |  }Ď  f d   }Đtd |Ď|Đ }Ńt^ t_ ta tb d tc d   tz ta tb d tc d   tb d tc d    ta  | | |# |   }Ň  f d   }Ótd |Ň|Ó }Ôt^ t_ t{ to ta tb d tc d   tb d tc d    ta  | | | |  }Ő  f d   }Ötd |Ő|Ö }×t^ t_ ta tb d tc d   t{ to ta tb d tc d   tb d tc d    ta  | | | |# |   }Ř  f d   }Ůtd |Ř|Ů }Út^ t_ ta tb d tc d   t{ to ta tb d tc d   tb d tc d    ta  | | | |# |  }Ű  f d   }Ütd |Ű|Ü }Ýt^ t_ tx ta tb d tc d   tb d tc d    tb d tc d   t{ tc d  ta tb d tc d   tb d tc d    ta  | | | |  }Ţ  f d   }ßtd |Ţ|ß }ŕt^ t_ t| ta tb d tc d   tb d tc d    tb d tc d   t{ tc d  ta tb d tc d   tb d tc d    ta  | | | | |$  }á  f d   }âtd |á|â }ăt^ t_ t} tc d  ta tb d tc d   tb d tc d    ta  | | |  }ä  f d   }ĺtd |ä|ĺ }ćt^ t_ t} t~ ta tb d tc d   tb d tc d    ta  | | |' |% |&  }ç  f d   }čtd |ç|č }ét^ t_ ta tb d tc d   t} tc d  ta tb d tc d   tb d tc d    ta  | | |#  }ę  f d   }ëtd |ę|ë }ět^ t_ ta tb d tc d   t} t~ ta tb d tc d   tb d tc d    ta  | | |' |% |& |# |   }í  f d   }îtd |í|î }ďt^ t_ ta tb d tc d   t} t~ ta tb d tc d   tb d tc d    ta  | | |' |% |& |# |  }đ  f d   }ńtd |đ|ń }ňt^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | |* |+ |( |)  }ó  f d   }ôtd |ó|ô }őt^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | |* |+ |( |,  }ö  f d   }÷td |ö|÷ }řt^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta tb d tc d   tb d tc d   ta  | | | | |. | |* |- 	 }ů  f d   }útd |ů|ú }űt^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta ta  | | | |* |+ |/  }ü  f d   }ýtd |ü|ý }ţt^ t_ ta tb d tc d   t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | | |* |+ | |( |) 	 }˙  f d   } td |˙|  }t^ t_ ta tb d tc d   t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | | |* |+ | |( |, 	 }  f d   }td || }t^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    t ta tb d tc d   tb d tc d    tb d tc d   ta ta  | | | | | |+ |2 |0 |1 
 }  f d   }td || }t^ t_ t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | | |* |( |)  }  f d   }	td ||	 }
t^ t_ ta tb d tc d   t to ta tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  | | | | |* |( |) | 	 }  f d   }td || }t^ t_ t to t ta tb d tc d   tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  |4 | | | | | |* |3 	 }  f d    }td || }t^ t_ ta tb dĄ tc d   tb d tc d   tb d tc d   t to t ta tb d tc d   tb d tc d   tb d tc d   tb d tc d   tb d tc d    ta  |4 | | | | |. |5 | |* |# |   }  f d˘   }td || }dŁ   }t^ t_ t t to t  ta  | | t |  }  f d¤   }td || }dĽ   }t^ t_ t t to t  t t  ta  | |6 t |  }  f dŚ   }td || }t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t ta  | | | |7 |8  }  f d§   }td || }t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   ta  | | | |9  }  f d¨   } td ||  }!t^ t_ ta tb d tc d   t ti ta tb d tc d    tb d tc d   tb d tc d   ta  | | | |* |  }"  f dŠ   }#td |"|# }$t^ t_ t ta to tb d tc d    tb d tc d   tb d tc d   ta  | | | |* |:  }%  f dŞ   }&td |%|& }'t^ t_ t ta to tb d tc d    tb d tc d   tb d tc d   ta  | | | |;  }(  f dŤ   })td |(|) }*t^ t_ t ta to tb d tc d    tb d tc d   tb d tc d   ta  | | |* |<  }+  f dŹ   },td |+|, }-t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   ta  | | | | |* | |=  }.  f d­   }/td |.|/ }0t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   ta  | | | | |* |>  }1  f dŽ   }2td |1|2 }3t^ t_ ta tb d tc d   t ta tb d tc d    tb d tc d   tb d tc d   ta  | | | |?  }4  f dŻ   }5td |4|5 }6t^ t_ ta tb d tc d   t ta to tb d tc d    tb d tc d   tb d tc d   ta  | | |* |@ |A |  }7  f d°   }8td |7|8 }9t^ t_ tc d  t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |B  }:  f dą   };td |:|; }<t^ t_ t ta tb d tc d   tb d tc d    t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |B  }=  f d˛   }>td |=|> }?t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |7 |C  }@  f dł   }Atd |@|A }Bt^ t_ tc d  t t ta tb d tc d   tb d tc d    tb d tc d   t ta tb d tc d   tb d tc d    ta  | | | |B  }C  f d´   }Dtd |C|D }Et^ t_ tc d  t t ta tb d tc d   tb d tc d    tb d tc d    t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |D  }F  f dľ   }Gtd |F|G }Ht^ t_ tc d  t t ta tb d tc d   tb d tc d    tb d tc d    t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |E  }I  f dś   }Jtd |I|J }Kt^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |7 |8  }L  f dˇ   }Mtd |L|M }Nt^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |* |F  }O  f d¸   }Ptd |O|P }Qt^ t_ ta tb d tc d   t t ti ta tb d tc d    tb d tc d   ta  | | | |  }R  f dš   }Std |R|S }Tt^ t_ ta tb d tc d   t ti ta tb d tc d    tb d tc d   tb d tc d   t t ti ta tb d tc d    tb d tc d   ta  | | | | |* |  }U  f dş   }Vtd |U|V }Wt^ t_ tc d  t t ta to tb d tc d    tb d tc d   ta  | | |<  }X  f dť   }Ytd |X|Y }Zt^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |* |G  }[  f dź   }\td |[|\ }]t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | |H |I  }^  f d˝   }_td |^|_ }`t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |H |J |K  }a  f dž   }btd |a|b }ct^ t_ t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |H |J |L  }d  f dż   }etd |d|e }ft^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |M |) |N  }g  f dŔ   }htd |g|h }it^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |M |) |O  }j  f dÁ   }ktd |j|k }lt^ t_ t ta to tb d tc d    tb d tc d   tb d tc d   t t ta to tb d tc d    tb d tc d   ta  | | | |* |<  }m  f dÂ   }ntd |m|n }ot^ t_ ta tb d tc d   t t ta tb d tc d    tb d tc d   ta  | | |# |   }p  f dĂ   }qtd |p|q }rt^ t_ tc d  ta t t ta tb d tc d    tb d tc d   ta  | | |P  }s  f dÄ   }ttd |s|t }ut^ t_ ta tb d tc d   t t ta tb d tc d    tb d tc d   ta  | | |# |  }v  f dĹ   }wtd |v|w }xt^ t_ ta tb d tc d   t t ta tb d tc d    tb d tc d   ta  | | | |  }y  f dĆ   }ztd |y|z }{t^ t_ tc d  ta t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |Q  }|  f dÇ   }}td |||} }~t^ t_ ta tb d tc d   t t ta to tb d tc d    tb d tc d   ta  | | |@ |A |  }  f dČ   }td || }t^ t_ t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   ta t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |* |R  }  f dÉ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | | |* | |S 	 }  f dĘ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | |T |U  }  f dË   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | | | |V |W |X 
 }  f dĚ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   t t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | | | |V |W |Y 
 }  f dÍ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | | |* | |Z |[ 
 }  f dÎ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | | | |* | |Z |\ 
 }  f dĎ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d    tb d tc d   ta  | | | | |* |  }  f dĐ   }td || }t^ t_ ta tb d tc d   t ta tb d tc d   tb d tc d    tb d tc d   tb d tc d   t t ta tb d tc d   tb d tc d    tb d tc d   ta  | | | |* | |@ |A  }  f dŃ   }td || }t^ t_ t ta  |]  }  f dŇ   }td || }|` |c |f |i |l |o |r |u |x |{ |~ | | | | | | | | | | | |˘ |Ľ |¨ |Ť |Ž |ą |´ |ˇ |ş |˝ |Ŕ |Ă |Ć |É |Ě |Ď |Ň |Ő |Ř |Ű |Ţ |á |ä |ç |ę |í |đ |ó |ö |ů |ü |˙ ||||||||||| |#|&|)|,|/|2|5|8|;|>|A|D|G|J|M|P|S|V|Y|\|_|b|e|h|k|n|q|t|w|z|}||||||||||||Ą|¤|§|Ş|­|°|ł|ś|š|ź|ż|Â|Ĺ|Č|Ë|Î|Ń|Ô|×|Ú|Ý|ŕ|ă|ć|é|ě|ď|ň|ő|ř|ű|ţ||||
|||||||!|$|'|*|-|0|3|6|9|<|?|B|E|H|K|N|Q|T|W|Z|]|`|c|f|i|l|o|r|u|x|{|~|||||||||||gŔ S(Ó   Ni˙˙˙˙(]   t   cons67t   cons2t   cons3t   cons66t   cons21t   cons1264t   cons7t   cons27t   cons17t   cons166t   cons1957t   cons1958t   cons94t   cons261t   cons1959t   cons1832t   cons62t   cons1960t   cons1961t   cons1962t   cons247t   cons1963t   cons1964t   cons1965t   cons1831t   cons4t   cons1255t   cons18t   cons1359t   cons1966t   cons1967t   cons168t   cons1968t   cons1969t   cons31t   cons1970t   cons1971t   cons1972t   cons800t   cons87t   cons88t   cons5t   cons50t   cons89t   cons383t   cons48t   cons1973t   cons1974t   cons1975t   cons52t   cons1976t   cons1099t   cons125t   cons1243t   cons13t   cons137t   cons1379t   cons1977t   cons1978t   cons196t   cons1979t   cons1980t   cons1981t   cons150t   cons463t   cons1765t   cons163t   cons948t   cons949t   cons1982t   cons1983t   cons803t   cons1984t   cons1985t   cons1986t   cons1987t   cons338t   cons1988t   cons1989t   cons1990t   cons1991t   cons1992t   cons1993t   cons38t   cons1994t   cons347t   cons1995t   cons1996t   cons1997t   cons1998t   cons1999t   cons2000t   cons2001t   bi   t   ai    c            sl     j  d  t t | | |  t d   t t  | |   t | | |  t | | |   | |   S(   NiS  i   (   t   appendR¤  t   expRŕ  Rá  t   PiRĚ  (   t   xR  R  (   t   rubi(    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6739   s    c            sm     j  d  t t | | |  t d   t t  | |   t | | |  t | | |   | |   S(   NiT  i   (   R  R¤  R  Rŕ  Rá  R  RŤ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6740   s    c            sl     j  d  t t | | |  t d   t t  | |   t | | |  t | | |   | |   S(   NiU  i   (   R  R¤  R  Rŕ  Rá  R  RŹ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6741   s    c      	      s     j  d  t t d  | |  t t t d  d t d  d  t t d  d t d  d  | t d  |  t d   t t  |   S(   NiV  i   i   i   (   R  R¤  Rŕ  RÖ  R   Rá  R  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6742   s    c            s<     j  d  t t | |   |  |   t t |   |   S(   NiW  (   R  R   RĚ  R¤  t   log(   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6743Ł   s    c      	      s     j  d  t t d  | |  t t t d  d t d  d  t t d  d t d  d  | t d  |  t d   t t  |   S(   NiX  i   i   i   (   R  R¤  Rŕ  RÖ  R   Rá  R  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6744¨   s    t   mc            sŻ     j  d  t t d  | t t  | t d  t |  | t d  t | | |  t d   |   |   t |  | t d  t | | |   | t d  |   S(   NiY  i   i   (	   R  RŔ  Rŕ  Rá  R  R   R  R¤  RĚ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6745­   s    c            sŽ     j  d  t t d  | t t  | t d  t |  | t d  t | | |  t d   |   |   t |  | t d  t | | |   | t d  |   S(   NiZ  i   i   (	   R  RŔ  Rŕ  Rá  R  R   R  R¤  RŤ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6746˛   s    c            sŽ     j  d  t t d  | t t  | t d  t |  | t d  t | | |  t d   |   |   t |  | t d  t | | |   | t d  |   S(   Ni[  i   i   (	   R  RŔ  Rŕ  Rá  R  R   R  R¤  RŹ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6747ˇ   s    i   t   dt   cc      	      sĹ     j  d  t |  t t  | t t | t d  t d  | |  | | | t d  |  t d  |  |  |  t t | |  |  t | | | t d   t d  | |  S(   Ni\  i   (	   R  RŔ  Rá  R  R   R  Rŕ  R¤  RĚ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6748ź   s    c      	      sÄ     j  d  t |  t t  | t t | t d  t d  | |  | | | t d  |  t d  |  |  |  t t | |  |  t | | | t d   t d  | |  S(   Ni]  i   (	   R  RŔ  Rá  R  R   R  Rŕ  R¤  RŤ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6749Á   s    c      	      sÄ     j  d  t |  t t  | t t | t d  t d  | |  | | | t d  |  t d  |  |  |  t t | |  |  t | | | t d   t d  | |  S(   Ni^  i   (	   R  RŔ  Rá  R  R   R  Rŕ  R¤  RŹ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6750Ć   s    c            sV    j  d  t |  t d  t d  | t | |  t d  t | | |  t | | | t d   |  |  t | t t  | t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   t d  | |  S(   Ni_  i˙˙˙˙i   iţ˙˙˙(	   R  RŔ  Rŕ  R   RĚ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6751Ë   s    c            sV    j  d  t |  t d  t d  | t | |  t d  t | | |  t | | | t d   |  |  t | t t  | t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   t d  | |  S(   Ni`  i˙˙˙˙i   iţ˙˙˙(	   R  RŔ  Rŕ  R   RŤ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6752Đ   s    c            sU    j  d  t |  t d  t d  | t | |  t d  t | | |  t | | | t d   |  |  t | t t  | t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   t d  | |  S(   Nia  i˙˙˙˙i   iţ˙˙˙(	   R  RŔ  Rŕ  R   RŹ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6753Ő   s    c      	      s     j  d  t t d  | | t t t d  d t d   t t d  d t d  d  |  | t d   t |  t t  |  S(   Nib  i   i   i   (   R  R¤  Rŕ  RÖ  R   R  Rá  R  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6754Ú   s    c      	      sm     j  d  t t | |  | t d   | |  t t | |  t | |  | t d   | |  S(   Nic  i   (   R  R   R  Rŕ  RĚ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6755ß   s    c      	      s     j  d  t t d  | | t t t d  d t d   t t d  d t d  d  |  | t d   t |  t t  |  S(   Nid  i   i   i   (   R  R¤  Rŕ  RÖ  R   R  Rá  R  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6756ä   s    c            sj    j  d  t t d  | |  t d  t | |  t d  t | | |  t | | | t d   |  |  t t d  | t t  |  t d  t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   |  t d  |  S(   Nie  i   i   (	   R  RŔ  Rŕ  R   RĚ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6757é   s    c            sj    j  d  t t d  | |  t d  t | |  t d  t | | |  t | | | t d   |  |  t t d  | t t  |  t d  t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   |  t d  |  S(   Nif  i   i   (	   R  RŔ  Rŕ  R   RŤ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6758î   s    c            si    j  d  t t d  | |  t d  t | |  t d  t | | |  t | | | t d   |  |  t t d  | t t  |  t d  t | |  t d  t | t d  t d  | | | | | t d  | t d  |  |  |  t | |  t d  t | | |  t | | | t d   |  t d  |  S(   Nig  i   i   (	   R  RŔ  Rŕ  R   RŹ  R  Rá  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6759ó   s    c            sŁ     j  d  t t d  t t  t | | |  t | | |   t | | |  t d   |   |   t | | |  t | | |   t d  | |   S(   Nih  i   i   (	   R  RŔ  Rŕ  Rá  R  R   RĚ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6760ř   s    c            s˘     j  d  t t d  t t  t | | |  t | | |   t | | |  t d   |   |   t | | |  t | | |   t d  | |   S(   Nii  i   i   (	   R  RŔ  Rŕ  Rá  R  R   RŤ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6761ý   s    c            s˘     j  d  t t d  t t  t | | |  t | | |   t | | |  t d   |   |   t | | |  t | | |   t d  | |   S(   Nij  i   i   (	   R  RŔ  Rŕ  Rá  R  R   RŹ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6762  s    c      	      sÉ     j  d  t t d  | t t  | t d  t |  | t d  t | |   t | t d  |  t d   |   |   t |  | t d  t | |   t d  | t d  |   S(   Nik  i   i   i   (	   R  RŔ  Rŕ  Rá  R  R   RĚ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6763  s    c      	      sČ     j  d  t t d  | t t  | t d  t |  | t d  t | |   t | t d  |  t d   |   |   t |  | t d  t | |   t d  | t d  |   S(   Nil  i   i   i   (	   R  RŔ  Rŕ  Rá  R  R   RŤ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6764  s    c      	      sČ     j  d  t t d  | t t  | t d  t |  | t d  t | |   t | t d  |  t d   |   |   t |  | t d  t | |   t d  | t d  |   S(   Nim  i   i   i   (	   R  RŔ  Rŕ  Rá  R  R   RŹ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6765  s    c            si     j  d  t t d  | t t | | |  | | t |   t d  |   |  | | |   |   S(   Nin  i   i   (   R  RŔ  Rŕ  R*   R   RĚ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6766  s    c            si     j  d  t t d  | t t | | |  | | t |   t d  |   |  | | |   |   S(   Nio  i   i   (   R  RŔ  Rŕ  R*   R   RŤ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6767  s    c            si     j  d  t t d  | t t | | |  | | t |   t d  |   |  | | |   |   S(   Nip  i   i   (   R  RŔ  Rŕ  R*   R   RŹ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6768   s    c            ss     j  d  t t t | | |  t d  t d   t | |   t | | |  t | | |   | |   S(   Niq  i   (   R  R¤  Ró  R  Rŕ  RŠ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6769%  s    c            st     j  d  t t t | | |  t d  t d   t | |   t | | |  t | | |   | |   S(   Nir  i   (   R  R¤  Rň  R  Rŕ  RŞ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6770*  s    c      
      s4    j  d  t t | |  t t t d  d t d  d  t t d  d t d  d  t t | t d  |  t d  t d   t d  |   t t | |  t t t d  d t d  d  t t d  d t d  d  t t | t d  |  t d  t d   t d  |   S(   Nis  i   i   i   (   R  R¤  Rç  RÖ  R   Rŕ  R  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6771/  s    c      
      s,    j  d  t | |  t t t d  d t d  d  t t d  d t d  d  t t | t d  |  t d  t d   t d  |   t | |  t t t d  d t d  d  t t d  d t d  d  t t | t d  |  t d  t d   t d  |   S(   Nit  i   i   i   (   R  R¤  RÖ  R   Rŕ  Rç  R  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement67724  s    c      	      s¨     j  d  t | | t d  t |  | t d  t t | | |  t d  t d   |   |   t |  | t d  t | | |   | t d  |   S(   Niu  i   i   (   R  RŔ  Rŕ  R   Rň  R  R¤  RŠ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement67739  s    c      	      s¨     j  d  t | | t d  t |  | t d  t t | | |  t d  t d   |   |   t |  | t d  t | | |   | t d  |   S(   Niv  i   i   (   R  RŔ  Rŕ  R   Ró  R  R¤  RŞ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6774>  s    c      	      sŚ     j  d  t t d  t | | |  t | | |   t t | | |  t d  t d   |   |   t | | |  t | | |   t d  | |   S(   Niw  i   (   R  RŔ  Rŕ  R   RŠ  Rň  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6775C  s    c      	      sŚ     j  d  t t d  t | | |  t | | |   t t | | |  t d  t d   |   |   t | | |  t | | |   t d  | |   S(   Nix  i   (   R  RŔ  Rŕ  R   RŞ  Ró  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6776H  s    c      	      sĚ     j  d  t t d  | | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t d  | t d  |   S(   Niy  i   i   (   R  RŔ  Rŕ  R   RŠ  Rň  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6777M  s    c      	      sĚ     j  d  t t d  | | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t d  | t d  |   S(   Niz  i   i   (   R  RŔ  Rŕ  R   RŞ  Ró  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6778R  s    c            sš     j  d  t t d  t d  t | t t t | t d  |  t d   |   |   t t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni{  i   i   (	   R  RŔ  Rŕ  R  R   Rň  R¤  RŠ  Ró  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6779W  s    c            sş     j  d  t t d  t d  t | t t t | t d  |  t d   |   |   t t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni|  i   i   (   R  RŔ  Rŕ  R  R   Rň  R¤  RŞ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6780\  s    c      
      s^    j  d  t t d  t d  t | t |  | t d  t t | t d  |  t d   |   |   t | t d  t | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni}  i   i   i˙˙˙˙iţ˙˙˙(	   R  RŔ  Rŕ  R  R   Rň  RŠ  Ró  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6781a  s    c      
      s_    j  d  t t d  t d  t | t |  | t d  t t | t d  |  t d   |   |   t | t d  t | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni~  i   i   i˙˙˙˙iţ˙˙˙(   R  RŔ  Rŕ  R  R   Rň  RŞ  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6782f  s    c      
      s    j  d  t | t d  | t d  t |  | t d  t t | t d  |  t d   |   |   t t | t d  | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t | |  | t d  t d  | t d  | t d  |   t |  | t d  t | |   t t | t d  |  t d  t d   | t d  |   S(   Ni  i   i   (	   R  RŔ  Rŕ  R   Ró  R  RŠ  R¤  Rň  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6783k  s    c      
      s     j  d  t | t d  | t d  t |  | t d  t t | t d  |  t d   |   |   t t | t d  | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t | |  | t d  t d  | t d  | t d  |   t |  | t d  t | |   t t | t d  |  t d  t d   | t d  |   S(   Ni  i   i   (	   R  RŔ  Rŕ  R   Ró  R  RŞ  Rň  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6784p  s    c            sŘ     j  d  t t d  t d  t | t t t | t d  |  t d   |   |   t |  t d  t | |   t t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni  i   i   (	   R  RŔ  Rŕ  R  R   Ró  R¤  RŠ  Rň  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6785u  s    c            sŘ     j  d  t t d  t d  t | t t t | t d  |  t d   |   |   t |  t d  t | |   t t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni  i   i   (   R  RŔ  Rŕ  R  R   Ró  R¤  RŞ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6786z  s    c      
      s    j  d  t t d  t d  t | t |  | t d  t t | t d  |  t d   |   |   t | t d  t | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | | |   t |  | t d  t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni  i   i   i˙˙˙˙iţ˙˙˙(	   R  RŔ  Rŕ  R  R   Ró  RŠ  Rň  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6787  s    c      
      s    j  d  t t d  t d  t | t |  | t d  t t | t d  |  t d   |   |   t | t d  t | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | | |   t |  | t d  t | |   t t | t d  |  t d  t d   t | t d  |   S(   Ni  i   i   i˙˙˙˙iţ˙˙˙(   R  RŔ  Rŕ  R  R   Ró  RŞ  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6788  s    c      
      s[    j  d  t | t d  | t d  t |  | t d  t t | t d  |  t d   |   |   t t | t d  | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t t | t d  |  t d  t d   | t d  |   S(   Ni  i   i   (	   R  RŔ  Rŕ  R   Rň  R  RŠ  R¤  Ró  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6789  s    c      
      s[    j  d  t | t d  | t d  t |  | t d  t t | t d  |  t d   |   |   t t | t d  | t d  t |  | t d  t | |   t t | t d  |  t d  t d   |   |   t |  | t d  t | |   t t | t d  |  t d  t d   | t d  |   S(   Ni  i   i   (	   R  RŔ  Rŕ  R   Rň  R  RŞ  Ró  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6790  s    c            s:     j  d  t t | t d  | | |   | |   S(   Ni  i   (   R  R¤  RĎ  Rŕ  (   R  R  t   nR  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6791  s    c            s     j  d  t | | t |  | t d  t | t d  | |   |   |   t |  | t | t d  | |   | |   S(   Ni  i˙˙˙˙i   (   R  RŔ  R   Rŕ  RĎ  R¤  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6792  s    c      
      s˛     j  d  t t t |   |   t | |  t t t d  t d  t d   t t d  t d  t d   | |   |   t t | |   t d  t d  |   S(   Ni  i   i   (   R  R¤  Rî  R  RÖ  R   Rŕ  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6793  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  RŔ  Rŕ  R   RĎ  R¤  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6794˘  s    c      	      sĐ     j  d  t |  | t d  t t | t d  | t d   t | t d  | t d   | |   | t d  t d  |   t |  | | |  | t | t d   t |   | |   S(   Ni  i   i   (   R  R¤  Rŕ  RÖ  R   R­  R  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6795§  s    c            sw     j  d  t |  | t d  t | | |   | | |   t |  | t d  t | | |   | | |   S(   Ni  i   (   R  R¤  Rŕ  RĎ  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6796Ź  s    c      	      s     j  d  t |  | t | |  t d  t | t d  | | |  |  |  t | |  t | t d  | | |  | |  S(   Ni  i˙˙˙˙i   (   R  RŔ  R   Rŕ  RĎ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6797ą  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  RŔ  Rŕ  R   RĎ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6798ś  s    c            sX     j  d  t t | | |   | |   t | | |  t | | |   | |   S(   Ni  (   R  R¤  R  RÎ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6799ť  s    c            s     j  d  t | | t d  t |  | t d  t | | |   | | |  |   |   t |  | t d  t | | |   | t d  |   S(   Ni  i   (   R  RŔ  Rŕ  R   R  R¤  RÎ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6800Ŕ  s    c            s     j  d  t t d  t t | | |   t | | |   |   |   t | | |  t | | |   t d  | |   S(   Ni  i   (   R  RŔ  Rŕ  R   RÎ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6801Ĺ  s    c            s     j  d  t t d  | t d  t |  | t | |   t | |   |   |   t |  | t d  t | |   t d  | t d  |   S(   Ni  i   i   (   R  RŔ  Rŕ  R   RÎ  R  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6802Ę  s    c      	      sD    j  d  t | | | | t d  t |  | t d  t | | |   t d  |   |   t t d  | t d  t |  | t | | |   t | | |   |   |   t |  | t d  t | | |   t d  | t d  |   t | |  | t | | |   t d  | | t d  |   S(   Ni  i   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RÎ  R  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6803Ď  s    c            s~     j  d  t | |  t t | | | |  |  | | | |  |  t t | | |  t | |  |  |  |  S(   Ni  (   R  RŔ  R   R  R¤  RÎ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6804Ô  s    c      	      sÝ     j  d  t | | t | |  t | | | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   Ni  i˙˙˙˙(   R  RŔ  R   R  Rŕ  RÎ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6805Ů  s    c      
      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   Ni  i   (   R  RŔ  Rŕ  R   RÎ  R  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6806Ţ  s    c            sh     j  d  t t t d  t | | |    | |   t | | |  t | | |   | |   S(   Ni  i   (   R  R¤  RÎ  Rŕ  R  RČ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6807ă  s    c            sD     j  d  t | |  |   t t | |   t | |   |   S(   Ni  (   R  R¤  RČ  R  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6808č  s    c            s     j  d  t | | t d  t |  | t d  t | | |   |   |   t |  | t d  t | | |   | t d  |   S(   Ni  i   (   R  RŔ  Rŕ  R   R  R¤  RČ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6809í  s    c            sW     j  d  t t | | |   | |   t | | |  t | | |   | |   S(   Ni  (   R  R¤  Ró  RÇ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6810ň  s    c            sX     j  d  t t | | |   | |   t | | |  t | | |   | |   S(   Ni  (   R  R¤  Rň  RĆ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6811÷  s    c      
      sě     j  d  t | |  t t t d  t d  t d   t t d  t d  t d   t | |   t d  |   t | |  t t t d  t d  t d   t t d  t d  t d   t | |   t d  |   S(   Ni  i   i   (   R  R¤  RÖ  R   Rŕ  Rç  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6812ü  s    c      
      s6    j  d  t t t |   |   t t | |  t t t d  t d  t d   t t d  t d  t d   t | |   t d  |   t t | |  t t t d  t d  t d   t t d  t d  t d   t | |   t d  |   t t | |   t d  t d  |   S(   Ni  i   i   (   R  R¤  Rî  R  Rç  RÖ  R   Rŕ  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6813  s    c            s     j  d  t | | t d  t |  | t d  t | | |   | | |  |   |   t |  | t d  t | | |   | t d  |   S(   Ni  i   (   R  RŔ  Rŕ  R   Rň  R¤  RÇ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6814  s    c            s     j  d  t | | t d  t |  | t d  t | | |   | | |  |   |   t |  | t d  t | | |   | t d  |   S(   Ni  i   (   R  RŔ  Rŕ  R   Ró  R¤  RĆ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6815  s    c            s     j  d  t t d  t t | | |   t | | |   |   |   t | | |  t | | |   t d  | |   S(   Ni   i   (   R  RŔ  Rŕ  R   RÇ  Rň  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6816  s    c            s     j  d  t t d  t t | | |   t | | |   |   |   t | | |  t | | |   t d  | |   S(   NiĄ  i   (   R  RŔ  Rŕ  R   RĆ  Ró  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6817  s    c            s     j  d  t t d  | t d  t |  | t | |   t | |   |   |   t |  | t d  t | |   t d  | t d  |   S(   Ni˘  i   i   (   R  RŔ  Rŕ  R   RÇ  Rň  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6818  s    c            s     j  d  t t d  | t d  t |  | t | |   t | |   |   |   t |  | t d  t | |   t d  | t d  |   S(   NiŁ  i   i   (   R  RŔ  Rŕ  R   RĆ  Ró  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6819  s    c      	      sD    j  d  t | | | | t d  t |  | t d  t | | |   t d  |   |   t t d  | t d  t |  | t | | |   t | | |   |   |   t |  | t d  t | | |   t d  | t d  |   t | |  | t | | |   t d  | | t d  |   S(   Ni¤  i   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RÇ  Rň  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6820$  s    c      	      sD    j  d  t | | | | t d  t |  | t d  t | | |   t d  |   |   t t d  | t d  t |  | t | | |   t | | |   |   |   t |  | t d  t | | |   t d  | t d  |   t | |  | t | | |   t d  | | t d  |   S(   NiĽ  i   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RĆ  Ró  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6821)  s    c            s     j  d  t | |  t t | | |  t | |  |  | | | |  |  t t | | |  t | |  |  |  |  S(   NiŚ  (   R  RŔ  R   Rň  Ró  R¤  RÇ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6822.  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   Ni§  (   R  RŔ  R   Rň  Ró  R¤  RĆ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement68233  s    c      	      sć     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   Ni¨  i˙˙˙˙(   R  RŔ  R   Rň  Ró  Rŕ  RÇ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement68248  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiŠ  i˙˙˙˙(   R  RŔ  R   Rň  Ró  Rŕ  RĆ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6825=  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiŞ  i   (   R  RŔ  Rŕ  R   RÇ  Ró  Rň  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6826B  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiŤ  i   (   R  RŔ  Rŕ  R   RĆ  Rň  Ró  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6827G  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   NiŹ  (   R  RŔ  R   Rň  R¤  RÇ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6828L  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   Ni­  (   R  RŔ  R   Ró  R¤  RĆ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6829Q  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiŽ  i˙˙˙˙(   R  RŔ  R   Rň  Rŕ  RÇ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6830V  s    c      	      sć     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiŻ  i˙˙˙˙(   R  RŔ  R   Ró  Rŕ  RĆ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6831[  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   Ni°  i   (   R  RŔ  Rŕ  R   RÇ  Rň  Ró  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6832`  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   Nią  i   (   R  RŔ  Rŕ  R   RĆ  Ró  Rň  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6833e  s    c            sX     j  d  t t | | |   | |   t | | |  t | | |   | |   S(   Ni˛  (   R  R¤  R˙  RÉ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6834j  s    c            sX     j  d  t t | | |   | |   t | | |  t | | |   | |   S(   Nił  (   R  R¤  R   RĘ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6835o  s    c      
      sä     j  d  t | |  t t t d  t d  t d   t t d  t d  t d   | |   t d  |   t | |  t t t d  t d  t d   t t d  t d  t d   | |   t d  |   S(   Ni´  i   i   (   R  R¤  RÖ  R   Rŕ  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6836t  s    c      
      s&    j  d  t t t |   |   t | |  t t t d  t d  t d   t t d  t d  t d   | |   t d  |   t | |  t t t d  t d  t d   t t d  t d  t d   | |   t d  |   t t | |   t d  t d  |   S(   Niľ  i   i   (   R  R¤  Rî  R  RÖ  R   Rŕ  (   R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6837y  s    c            s     j  d  t | | t d  t |  | t d  t | | |   | | |  |   |   t |  | t d  t | | |   | t d  |   S(   Niś  i   (   R  RŔ  Rŕ  R   R   R¤  RÉ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6838~  s    c            s     j  d  t | | t d  t |  | t d  t | | |   | | |  |   |   t |  | t d  t | | |   | t d  |   S(   Niˇ  i   (   R  RŔ  Rŕ  R   R˙  R¤  RĘ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6839  s    c            s     j  d  t t d  t t | | |   t | | |   |   |   t | | |  t | | |   t d  | |   S(   Ni¸  i   (   R  RŔ  Rŕ  R   RÉ  R   R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6840  s    c            s     j  d  t t d  t t | | |   t | | |   |   |   t | | |  t | | |   t d  | |   S(   Niš  i   (   R  RŔ  Rŕ  R   RĘ  R˙  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6841  s    c            s     j  d  t t d  | t d  t |  | t | |   t | |   |   |   t |  | t d  t | |   t d  | t d  |   S(   Niş  i   i   (   R  RŔ  Rŕ  R   RÉ  R   R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6842  s    c            s     j  d  t t d  | t d  t |  | t | |   t | |   |   |   t |  | t d  t | |   t d  | t d  |   S(   Niť  i   i   (   R  RŔ  Rŕ  R   RĘ  R˙  R¤  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6843  s    c      	      sD    j  d  t | | | | t d  t |  | t d  t | | |   t d  |   |   t t d  | t d  t |  | t | | |   t | | |   |   |   t |  | t d  t | | |   t d  | t d  |   t | |  | t | | |   t d  | | t d  |   S(   Niź  i   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RÉ  R   R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6844  s    c      	      sD    j  d  t | | | | t d  t |  | t d  t | | |   t d  |   |   t t d  | t d  t |  | t | | |   t | | |   |   |   t |  | t d  t | | |   t d  | t d  |   t | |  | t | | |   t d  | | t d  |   S(   Ni˝  i   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RĘ  R˙  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6845Ą  s    c            s     j  d  t | |  t t | | |  t | |  |  | | | |  |  t t | | |  t | |  |  |  |  S(   Niž  (   R  RŔ  R   R   R˙  R¤  RÉ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6846Ś  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   Niż  (   R  RŔ  R   R   R˙  R¤  RĘ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6847Ť  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiŔ  i˙˙˙˙(   R  RŔ  R   R   R˙  Rŕ  RÉ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6848°  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiÁ  i˙˙˙˙(   R  RŔ  R   R   R˙  Rŕ  RĘ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6849ľ  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiÂ  i   (   R  RŔ  Rŕ  R   RÉ  R˙  R   R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6850ş  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiĂ  i   (   R  RŔ  Rŕ  R   RĘ  R   R˙  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6851ż  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   NiÄ  (   R  RŔ  R   R   R¤  RÉ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6852Ä  s    c            s     j  d  t | |  t t | |  |  t | | |  | | | |  |  t t | | |  t | |  |  |  |  S(   NiĹ  (   R  RŔ  R   R˙  R¤  RĘ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6853É  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiĆ  i˙˙˙˙(   R  RŔ  R   R   Rŕ  RÉ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6854Î  s    c      	      sç     j  d  t | | t | |  t | | |  t | | |  | | | |  |  t |  | t | |  t d  t | | |  t | | |  |  |  t | |  t | | |  t | | |  | |  S(   NiÇ  i˙˙˙˙(   R  RŔ  R   R˙  Rŕ  RĘ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6855Ó  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiČ  i   (   R  RŔ  Rŕ  R   RÉ  R   R˙  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6856Ř  s    c      	      s    j  d  t | |  t d  t | |  t d  t | | |  t | | |  |  |  t | |  t d  t | |  t d  t | | |  t | | |  | | | |  |  t | |  t d  t | | |  t | | |  |  t d  |  S(   NiÉ  i   (   R  RŔ  Rŕ  R   RĘ  R˙  R   R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6857Ý  s    c            sh     j  d  t t | t d  | | |   | |   t | | |  t | | | |   | |   S(   NiĘ  i   (   R  R¤  R­  Rŕ  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6858â  s    c      
      s     j  d  t t |  t |   |   t | |  | t t | |  t | t d  | t d   | |   | t d  |   S(   NiË  i   i   (   R  R¤  R­  R  RÖ  R   Rŕ  (   R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6859ç  s    c            s     j  d  t |  | t d  t | | |   | t d  |   t |  | | |  | t | | t d  | |   | | t d  |   S(   NiĚ  i   (   R  R¤  Rŕ  R­  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6860ě  s    c            sł   t  }   j d  t | |  t d  t | |  t d  | | | | t d  t | | |  |  |  t | |  t d  t | | | |  |  t d  |  S(   NiÍ  i   i˙˙˙˙(   t   TrueR  RŔ  Rŕ  R   R  R¤  R­  (   R  R  R  RĆ  R  t	   _UseGamma(   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   With6861đ  s    c            s5     j  d  t t t d  | | |   | |   S(   NiÎ  iţ˙˙˙(   R  R¤  RÍ  Rŕ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6862÷  s    c      	      s     j  d  t | | t |  | t d  t t d  | | |   |   |   t |  | t t d  | | |   | |   S(   NiĎ  i˙˙˙˙iţ˙˙˙(   R  RŔ  R   Rŕ  RÍ  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6863ü  s    c            s9     j  d  t t | t d  | | |   | |   S(   NiĐ  i˙˙˙˙(   R  R¤  RÍ  Rŕ  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6864  s    c      	      s     j  d  t |  | t | |  t d  t | t d  | | |  |  |  t | |  t | t d  | | |  | |  S(   NiŃ  i˙˙˙˙(   R  RŔ  R   Rŕ  RÍ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6865  s    c      	      s      j  d  t | |  t d  t | |  t d  t | t d  | | |  |  |  t | |  t d  t | | | |  |  t d  |  S(   NiŇ  i   (   R  RŔ  Rŕ  R   RÍ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6866  s    RĆ  c            s4     j  d  t t | | |   | | | |   S(   NiÓ  (   R  R¤  R­  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6867  s    c            s4     j  d  t t | |  |  | |  | |  S(   NiÔ  (   R  R¤  RŇ  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6868  s    c            s1     j  d  t t t d  | | |   |   S(   NiŐ  i   (   R  R   RÍ  Rŕ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6869  s    c            sH     j  d  t t | t d  | | |   | | t d  |   S(   NiÖ  i˙˙˙˙(   R  R¤  RÓ  Rŕ  (   R  R  R  t   s(   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6870  s    c            s9     j  d  t |  | t t d  | | |   |   S(   Ni×  i   (   R  R   RÍ  Rŕ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6871$  s    c      	      s§     j  d  t |  | | t d  t | |  t d  t | t d  | | |  |  |  t | |  t | t d  | | |  | | t d  |  S(   NiŘ  i˙˙˙˙(   R  RŔ  Rŕ  R   RÓ  R¤  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6872)  s    c      	      sŁ     j  d  t | | |  t d  t | |  t d  t | t d  | | |  |  |  t | |  t d  t | | | |  |  t d  |  S(   NiŮ  i   (   R  RŔ  Rŕ  R   RÓ  R¤  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6873.  s    t   pt   qc      	      sx     j  d  t |  | t t | t d  | | | |  |  |  |  t | t | | | | |  |  |  S(   NiÚ  i˙˙˙˙(   R  RŔ  R   Rž  Rŕ  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement68743  s    c      	      s     j  d  t t d  |  | t t | t d  | | | |  |  |  |  t | t | t d  | | | |  |  |  | |  S(   NiŰ  i   (   R  RŔ  Rŕ  R   Rž  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement68758  s    t   ec            sE     j  d  t t | t d  | | | | |   | |  |  S(   NiÜ  i   (   R  R¤  Rž  Rŕ  (   R  R  R  R  R  RĆ  R  R!  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6876=  s    c            sE     j  d  t t | t d  | | | |  |  |  | |  S(   NiÝ  i   (   R  R¤  Rž  Rŕ  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6877B  s    c      
      sŞ     j  d  t |  | | t d  t | | t | t d  | | | |  |  |  |  t | | t d  t | | | | |  |  | t d  |  S(   NiŢ  i   i˙˙˙˙(   R  RŔ  Rŕ  R   Rž  R¤  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6878G  s    c      
      sŽ     j  d  t | t d  |  | t | | t | t d  | | | |  |  |  |  t | | t d  t | t d  | | | |  |  |  | |  S(   Niß  i   (   R  RŔ  Rŕ  R   Rž  R¤  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6879L  s    t   rc	   	   	      sČ     j  d  t | | |  | t t | t d  | | | |  |  t | | |  | t d  | |  |  t t | t d  | | | |  |  t | | |  | |  | |  S(   Niŕ  i   i˙˙˙˙(   R  RŔ  R   Rž  Rŕ  R  R¤  (	   R  R  R  R&  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6880Q  s    c      
      sŔ     j  d  t |  t t | t d  | | | | |   |  |  t | |  t t | t d  | | | | |   | | | |  |  t | t | | | | | |   |  S(   Niá  i˙˙˙˙(   R  RŔ  R   Rž  Rŕ  R¤  (   R  R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6881V  s    c      
      sŔ     j  d  t | |  | t d  t | | t d  t | t d  | | | | |   | | | |  |  t | | t d  t | | | | | |   | t d  |  S(   Niâ  i   i˙˙˙˙(   R  RŔ  Rŕ  R   Rž  R¤  (   R  R  R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6882[  s    c      	      s[     j  d  t t | t d  | | | | | | |   | | |  t |  |  S(   Niă  i   (   R  R¤  Rž  Rŕ  R  (   R  R  R  R  R  RĆ  R  t   F(   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6883`  s    t   fc            sä     j  d  t | | | | |  t |	  t |
 | | | t d  t | t d  | |	 | | | | |   |  |  t |
 | | | t | t d  | |	 | | | | |   | | |  t |	  |  S(   Niä  i˙˙˙˙i   (   R  RŔ  R  R   Rŕ  Rž  R¤  (   R  R  R,  R  R  R  R  RĆ  R  R*  R!  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6884e  s    c         S   st   t  | t t t t f  r t Sy, t |  | |  |  } t t |   } Wn t	 t
 f k
 re t SX| rp t St S(   N(   t
   isinstancet   intRä  t   floatRĺ  t   FalseRŐ  R5   R   t	   TypeErrort   AttributeErrorR  (   t   vR  RĆ  t   ut   wt   res(    (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   With6885i  s    c            sG   t  |  | |  |  }   j d  t | t | t d  |   |  S(   Niĺ  i   (   RŐ  R  R¤  Rž  Rŕ  (   R4  R  RĆ  R5  R6  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6885u  s    c         S   st   t  | t t t t f  r t Sy, t |  | |  |  } t t |   } Wn t	 t
 f k
 re t SX| rp t St S(   N(   R.  R/  Rä  R0  Rĺ  R1  RŐ  R5   R   R2  R3  R  (   R4  R6  R5  RĆ  R  t   zR7  (    (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   With6886{  s    c            s   t  |  | |  |  }   j d  t t | t | |  t | t d  |   | |  |  t | t | t d  |   t |  |  S(   Nić  i   (	   RŐ  R  R   R,  Rż  Rž  Rŕ  R¤  R  (   R4  R6  R5  RĆ  R  R:  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6886  s    c            sľ     j  d  t |  | |  t d  t | t | | |  |  t d  t | | |  t d  |  |  t | t | | |  |  | | | | |  t d  |  S(   Niç  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6887  s    c            s     j  d  t |  t | t | | |  |  t | | |  t d  |  |  t | t | | |  |  | | | | |  S(   Nič  i   (   R  RŔ  R   RÔ  Rŕ  R¤  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6888  s    c      	      so     j  d  t t d  | t t t | t |  |  | | | | | |  |  | | | |  |  S(   Nié  i   (   R  RŔ  Rŕ  R*   R   RĘ   RÔ  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6889  s    c            s     j  d  t | |  t | t | | |  |  t | | |  t d  |  |  t | | t | | |  |  |  S(   Nię  i   (   R  RŔ  R   RÔ  Rŕ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6890  s    c            sľ     j  d  t | |  | | |  t d  t | t | | |  |  t d  t | | |  t d  |  |  t | | t | | |  |  | |  t d  |  S(   Nië  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6891˘  s    c            sV     j  d  t t | t | | |  |  | t d  |  | t d  |  S(   Niě  i   i   (   R  R*   R   RÔ  Rŕ  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6892§  s    c      	      sś     j  d  t | |  | t d  t | | | t | | |  |  t | | |  t d  |  |  t | | t d  | t | | |  |  | t d  |  S(   Nií  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6893Ź  s    c      	      sÓ     j  d  t | |  | | | |  t d  t | | | t | | |  |  t d  t | | |  t d  |  |  t | | t d  | t | | |  |  | | |  t d  |  S(   Niî  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6894ą  s    c            sŤ     j  d  t t d  | t | | | t | |  |  t d  t | |  t d  |  |  t | | | t | |  |  t | |  t d  |  S(   Niď  i   (   R  RŔ  Rŕ  R   RÔ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6895ś  s    c            s[     j  d  t t | | t d  | t | | |  |  |  | t d  |  S(   Niđ  iţ˙˙˙i   (   R  R*   R   Rŕ  RÔ  (   R  R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6896ť  s    c            s<     j  d  t | | | | |  t | | |  |  S(   Niń  (   R  R¤  RÔ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6897Ŕ  s    c            sL     j  d  t t d  |  t | | |  |  |  t |  | |  S(   Niň  i   (   R  R   Rŕ  RÔ  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6898Ĺ  s    c      	      sŞ     j  d  t | |  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  t d  | | | | | |  S(   Nió  i˙˙˙˙(   R  RŔ  R   RÔ  Rŕ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6899Ę  s    c            s6     j  d  t t t | | |   | |  |  S(   Niô  (   R  R¤  RÎ  RÔ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6900Ď  s    c            sn     j  d  t t t | t | |  |   t | t d    t t | t d   |  | | |  S(   Niő  i   (   R  R¤  RŹ  Rá  RÔ  R  Rŕ  R  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6901Ô  s    c            sp     j  d  t t t | t | |  |   t | t d    t t | t d   |  | | |  S(   Niö  i   (   R  R¤  RĚ  Rá  RÔ  R  Rŕ  R  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6902Ů  s    c      	      sž     j  d  t t d  | |  t d  t | t | | |  |  t d  | t | | |  | |  |  t | t | | |  |  | | | | | |  t d  |  S(   Ni÷  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6903Ţ  s    c            sv     j  d  t t | | |  |  | t | | |  |  t |  t d  t | | |   | | |  S(   Niř  i   (   R  R¤  RÔ  R­  Rŕ  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6904ă  s    c      	      sy     j  d  t t d  | t t t t d  | t |  | | | | | |  |  |  | | | |  |  S(   Niů  i   (   R  RŔ  Rŕ  R*   R   RĘ   RÔ  (   R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6905č  s    c      	      s     j  d  t t d  | t t t | t |  |  | t |  | | | | | | |  |  | | | |  |  S(   Niú  i   (   R  RŔ  Rŕ  R*   R   RĘ   RÔ  (   R  R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6906í  s    c      	      s`     j  d  t t t d  | t d  |  t | | |  |  |  | t d  |  S(   Niű  i   i   (   R  R*   R   Rŕ  RÔ  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6907ň  s    c            sF     j  d  t | | | t | | |  |  t d  | |  S(   Niü  i˙˙˙˙(   R  R¤  RÔ  Rŕ  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6908÷  s    c            sC     j  d  t | |  t |  t | | |   | | |  S(   Niý  (   R  R¤  RÎ  RÔ  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6909ü  s    c      	      s     j  d  t | t d  | | t d  | t t | t | | |   t | | t d    t t | | t d   | | |  S(   Niţ  i   i   (   R  R¤  Rŕ  RŹ  Rá  RÔ  R  R  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6910  s    c      	      s     j  d  t | t d  | | t d  | t t | t | | |   t | | t d    t t | | t d   | | |  S(   Ni˙  i   i   (   R  R¤  Rŕ  RĚ  Rá  RÔ  R  R  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6911  s    c      	      sś     j  d  t | | |  t d  t d  t | t | | |  |  t d  | t | | |  | |  |  t | | | t | | |  |  t d  | |  S(   Ni   i˙˙˙˙i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6912  s    c      	      sş     j  d  t t d  | | |  t d  t | t | | |  |  t d  | t | | |  | |  |  t | | t | | |  |  | | |  t d  |  S(   Ni  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6913  s    c      	      sq     j  d  t t | t | | |  |  | t d  | t | | |  | |  | t d  |  S(   Ni  i   i   (   R  R*   R   RÔ  Rŕ  (   R  R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6914  s    c            s     j  d  t | | t d  t | | |  t | |  |  t | |  |  |  t | | t d  |  | t d  t | |  |  S(   Ni  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6915  s    c            s.     j  d  t t t | |   |  |  S(   Ni  (   R  R¤  R  RÔ  (   R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6916  s    c            sp     j  d  t | | t | |  |  t | |  |  |  t | | t d  |  | t d  |  S(   Ni  i   (   R  R   RÔ  R¤  Rŕ  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6917$  s    c            s     j  d  t | | | t d  t | |  | t | t d  | t d  t | |   t | t | |   | |  | t d  |  S(   Ni  i   (   R  R¤  Rŕ  RÔ  R­  R  (   R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6918)  s    c            s6     j  d  t t t | | |   |  | |  S(   Ni  (   R  R¤  R  RÔ  (   R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6919.  s    c            s[     j  d  t t | |  t d  | t | | |  | |  | t d  |  S(   Ni  iţ˙˙˙i   (   R  R*   R   Rŕ  RÔ  (   R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement69203  s    c            s<     j  d  t | t | | |  |  | | |  |  S(   Ni	  (   R  R¤  RÔ  (   R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement69218  s    c            sb     j  d  t | | | t d  | t | | |  |  t d  | | t d  |  S(   Ni
  i   i˙˙˙˙(   R  R¤  Rŕ  RÔ  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6922=  s    c            sC     j  d  t | |  t |  t | | |   | | |  S(   Ni  (   R  R¤  RÎ  RÔ  (   R  R  R  R  RĆ  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6923B  s    c      	      sş     j  d  t | |  t d  d | |  t d  d t t | t | | |   t | |  t d  d t d    t t | |  t d  d t d   | | |  S(   Ni  i˙˙˙˙i   (   R  R¤  Rŕ  RĚ  Rá  RÔ  R  R  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6924G  s    c      	      sź     j  d  t | |  t d  d | |  t d  d t t | t | | |   t | |  t d  d t d    t t | |  t d  d t d   | | |  S(   Ni  i˙˙˙˙i   (   R  R¤  Rŕ  RŹ  Rá  RÔ  R  R  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6925L  s    c      	      sě     j  d  t | | | |  t d  t d  | t d  t | | | t | | |  |  t d  | t | | |  | |  |  t | | | t d  | t | | |  |  t d  | | t d  |  S(   Ni  i˙˙˙˙i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6926Q  s    c      	      sÜ     j  d  t | t d  | | | |  t d  t | | | t | | |  |  t d  | t | | |  | |  |  t | | t d  | t | | |  |  | | | |  t d  |  S(   Ni  i   (   R  RŔ  Rŕ  R   RÔ  R¤  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6927V  s    c            s˝     j  d  t | | | t | |  |  | t d  t | |  | |  t | |  t d  | t d  t | |   t | t | |   | | | t d  |  S(   Ni  i   (   R  R¤  RÔ  Rŕ  R­  R  (   R  R  R  R  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6928[  s    c            sv     j  d  t t | | t d  | t | | |  |  | t | | |  | |  | t d  |  S(   Ni  iţ˙˙˙i   (   R  R*   R   Rŕ  RÔ  (   R  R  R  R  RĆ  R  R  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6929`  s    c            s_     j  d  t t t |  t d  t t |   | |   t |   |   |   |  t |    S(   Ni  i   (   R  R*   R   R,  Rŕ  R¨  RÔ  R  (   R  R5  (   R  (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   replacement6930e  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   Rß  RĚ  t   x_Rď  Rŕ  R   RŤ  RŹ  R  t   m_t   a_RŠ  RŞ  Rň  Ró  RĎ  t   n_RÎ  RČ  RÇ  RĆ  RÉ  RĘ  R   R˙  R­  t   b_RĐ  RÍ  RŇ  RÓ  t   s_Rž  R  t   F_t   u_t   v_R   t   w_RÔ  t   p_t   d_Rá  (   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  t   pattern6739R  t   rule6739t   pattern6740R  t   rule6740t   pattern6741R  t   rule6741t   pattern6742R  t   rule6742t   pattern6743R  t   rule6743t   pattern6744R  t   rule6744t   pattern6745R  t   rule6745t   pattern6746R  t   rule6746t   pattern6747R  t   rule6747t   pattern6748R  t   rule6748t   pattern6749R  t   rule6749t   pattern6750R  t   rule6750t   pattern6751R  t   rule6751t   pattern6752R  t   rule6752t   pattern6753R   t   rule6753t   pattern6754RĄ  t   rule6754t   pattern6755R˘  t   rule6755t   pattern6756RŁ  t   rule6756t   pattern6757R¤  t   rule6757t   pattern6758RĽ  t   rule6758t   pattern6759RŚ  t   rule6759t   pattern6760R§  t   rule6760t   pattern6761R¨  t   rule6761t   pattern6762RŠ  t   rule6762t   pattern6763RŞ  t   rule6763t   pattern6764RŤ  t   rule6764t   pattern6765RŹ  t   rule6765t   pattern6766R­  t   rule6766t   pattern6767RŽ  t   rule6767t   pattern6768RŻ  t   rule6768t   pattern6769R°  t   rule6769t   pattern6770Rą  t   rule6770t   pattern6771R˛  t   rule6771t   pattern6772Rł  t   rule6772t   pattern6773R´  t   rule6773t   pattern6774Rľ  t   rule6774t   pattern6775Rś  t   rule6775t   pattern6776Rˇ  t   rule6776t   pattern6777R¸  t   rule6777t   pattern6778Rš  t   rule6778t   pattern6779Rş  t   rule6779t   pattern6780Rť  t   rule6780t   pattern6781Rź  t   rule6781t   pattern6782R˝  t   rule6782t   pattern6783Rž  t   rule6783t   pattern6784Rż  t   rule6784t   pattern6785RŔ  t   rule6785t   pattern6786RÁ  t   rule6786t   pattern6787RÂ  t   rule6787t   pattern6788RĂ  t   rule6788t   pattern6789RÄ  t   rule6789t   pattern6790RĹ  t   rule6790t   pattern6791RÇ  t   rule6791t   pattern6792RČ  t   rule6792t   pattern6793RÉ  t   rule6793t   pattern6794RĘ  t   rule6794t   pattern6795RË  t   rule6795t   pattern6796RĚ  t   rule6796t   pattern6797RÍ  t   rule6797t   pattern6798RÎ  t   rule6798t   pattern6799RĎ  t   rule6799t   pattern6800RĐ  t   rule6800t   pattern6801RŃ  t   rule6801t   pattern6802RŇ  t   rule6802t   pattern6803RÓ  t   rule6803t   pattern6804RÔ  t   rule6804t   pattern6805RŐ  t   rule6805t   pattern6806RÖ  t   rule6806t   pattern6807R×  t   rule6807t   pattern6808RŘ  t   rule6808t   pattern6809RŮ  t   rule6809t   pattern6810RÚ  t   rule6810t   pattern6811RŰ  t   rule6811t   pattern6812RÜ  t   rule6812t   pattern6813RÝ  t   rule6813t   pattern6814RŢ  t   rule6814t   pattern6815Rß  t   rule6815t   pattern6816Rŕ  t   rule6816t   pattern6817Rá  t   rule6817t   pattern6818Râ  t   rule6818t   pattern6819Ră  t   rule6819t   pattern6820Rä  t   rule6820t   pattern6821Rĺ  t   rule6821t   pattern6822Rć  t   rule6822t   pattern6823Rç  t   rule6823t   pattern6824Rč  t   rule6824t   pattern6825Ré  t   rule6825t   pattern6826Rę  t   rule6826t   pattern6827Rë  t   rule6827t   pattern6828Rě  t   rule6828t   pattern6829Rí  t   rule6829t   pattern6830Rî  t   rule6830t   pattern6831Rď  t   rule6831t   pattern6832Rđ  t   rule6832t   pattern6833Rń  t   rule6833t   pattern6834Rň  t   rule6834t   pattern6835Ró  t   rule6835t   pattern6836Rô  t   rule6836t   pattern6837Rő  t   rule6837t   pattern6838Rö  t   rule6838t   pattern6839R÷  t   rule6839t   pattern6840Rř  t   rule6840t   pattern6841Rů  t   rule6841t   pattern6842Rú  t   rule6842t   pattern6843Rű  t   rule6843t   pattern6844Rü  t   rule6844t   pattern6845Rý  t   rule6845t   pattern6846Rţ  t   rule6846t   pattern6847R˙  t   rule6847t   pattern6848R   t   rule6848t   pattern6849R  t   rule6849t   pattern6850R  t   rule6850t   pattern6851R  t   rule6851t   pattern6852R  t   rule6852t   pattern6853R  t   rule6853t   pattern6854R  t   rule6854t   pattern6855R  t   rule6855t   pattern6856R  t   rule6856t   pattern6857R	  t   rule6857t   pattern6858R
  t   rule6858t   pattern6859R  t   rule6859t   pattern6860R  t   rule6860R  t   pattern6861t   rule6861t   pattern6862R  t   rule6862t   pattern6863R  t   rule6863t   pattern6864R  t   rule6864t   pattern6865R  t   rule6865t   pattern6866R  t   rule6866t   pattern6867R  t   rule6867t   pattern6868R  t   rule6868t   pattern6869R  t   rule6869t   pattern6870R  t   rule6870t   pattern6871R  t   rule6871t   pattern6872R  t   rule6872t   pattern6873R  t   rule6873t   pattern6874R  t   rule6874t   pattern6875R   t   rule6875t   pattern6876R"  t   rule6876t   pattern6877R#  t   rule6877t   pattern6878R$  t   rule6878t   pattern6879R%  t   rule6879t   pattern6880R'  t   rule6880t   pattern6881R(  t   rule6881t   pattern6882R)  t   rule6882t   pattern6883R+  t   rule6883t   pattern6884R-  t   rule6884R8  t   pattern6885R9  t   rule6885R;  t   pattern6886R<  t   rule6886t   pattern6887R=  t   rule6887t   pattern6888R>  t   rule6888t   pattern6889R?  t   rule6889t   pattern6890R@  t   rule6890t   pattern6891RA  t   rule6891t   pattern6892RB  t   rule6892t   pattern6893RC  t   rule6893t   pattern6894RD  t   rule6894t   pattern6895RE  t   rule6895t   pattern6896RF  t   rule6896t   pattern6897RG  t   rule6897t   pattern6898RH  t   rule6898t   pattern6899RI  t   rule6899t   pattern6900RJ  t   rule6900t   pattern6901RK  t   rule6901t   pattern6902RL  t   rule6902t   pattern6903RM  t   rule6903t   pattern6904RN  t   rule6904t   pattern6905RO  t   rule6905t   pattern6906RP  t   rule6906t   pattern6907RQ  t   rule6907t   pattern6908RR  t   rule6908t   pattern6909RS  t   rule6909t   pattern6910RT  t   rule6910t   pattern6911RU  t   rule6911t   pattern6912RV  t   rule6912t   pattern6913RW  t   rule6913t   pattern6914RX  t   rule6914t   pattern6915RY  t   rule6915t   pattern6916RZ  t   rule6916t   pattern6917R[  t   rule6917t   pattern6918R\  t   rule6918t   pattern6919R]  t   rule6919t   pattern6920R^  t   rule6920t   pattern6921R_  t   rule6921t   pattern6922R`  t   rule6922t   pattern6923Ra  t   rule6923t   pattern6924Rb  t   rule6924t   pattern6925Rc  t   rule6925t   pattern6926Rd  t   rule6926t   pattern6927Re  t   rule6927t   pattern6928Rf  t   rule6928t   pattern6929Rg  t   rule6929t   pattern6930Rh  t   rule6930(    (   R  sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   special_functions   s   ˙ ˙ :JJJ888dddrrrTTT[[[\\\JJ88ddTTLLbboooobbooooPQAEHT[[JdTU\J8dJJ88ddTTUU\\JJ88ddTTUU\\M/E^JdPjjSSjpp||ŹĚ|ß	1	;gs~gddwnąşşąŔlš\Ŕ§ąąŔŔh\hhroÄÝÄŃŃŕŕąÚ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$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   R:   R;   R<   R=   R>   R?   R@   RA   RB   RC   RD   RE   RF   RG   RH   RI   RJ   RK   RL   RM   RN   RO   RP   RQ   RR   RS   RT   RU   RV   RW   RX   RY   RZ   R[   R\   R]   R^   R_   R`   Ra   Rb   Rc   Rd   Re   Rf   Rg   Rh   Ri   Rj   Rk   Rl   Rm   Rn   Ro   Rp   Rq   Rr   Rs   Rt   Ru   Rv   Rw   Rx   Ry   Rz   R{   R|   R}   R~   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    RĄ   R˘   RŁ   R¤   RĽ   RŚ   R§   R¨   RŠ   RŞ   RŤ   RŹ   R­   RŽ   RŻ   R°   Rą   R˛   Rł   R´   Rľ   Rś   Rˇ   R¸   Rš   Rş   Rť   Rź   R˝   Rž   Rż   RŔ   RÁ   RÂ   RĂ   RÄ   RĹ   RĆ   RÇ   RČ   RÉ   RĘ   RË   RĚ   RÍ   RÎ   RĎ   RĐ   RŃ   RŇ   RÓ   RÔ   RŐ   RÖ   R×   RŘ   RŮ   RÚ   RŰ   RÜ   RÝ   RŢ   Rß   Rŕ   Rá   Râ   Ră   Rä   Rĺ   Rć   Rç   Rč   Ré   Rę   Rë   Rě   Rí   Rî   Rď   Rđ   Rń   Rň   Ró   Rô   Rő   Rö   R÷   Rř   Rů   Rú   Rű   Rü   Rý   Rţ   R˙   R   R  R  R  R  R  R  R  R  R	  R
  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R  R   R!  R"  R#  R$  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   RĄ  R˘  RŁ  R¤  RĽ  RŚ  R§  R¨  RŠ  RŞ  RŤ  RŹ  R­  RŽ  RŻ  R°  Rą  R˛  Rł  R´  Rľ  Rś  Rˇ  R¸  Rš  Rş  Rť  Rź  R˝  Rž  Rż  RŔ  RÁ  RÂ  RĂ  RÄ  RĹ  RĆ  RÇ  RČ  RÉ  RĘ  RË  RĚ  RÍ  RÎ  RĎ  RĐ  RŃ  RŇ  RÓ  RÔ  RŐ  RÖ  R×  RŘ  RŮ  RÚ  R  RŰ  R  RÜ  RÝ  RŢ  t   sympyRß  Rŕ  Rá  Râ  Ră  Rä  Rĺ  Rć  Rç  Rč  Ré  Rę  Rë  Rě  Rí  Rî  t   sympy.integrals.rubi.symbolRď  t   sympy.core.symbolRđ  Rń  t   sympy.functionsRň  Ró  Rô  Rő  Rö  R÷  Rř  t%   sympy.functions.elementary.hyperbolicRů  Rú  Rű  Rü  Rý  Rţ  R˙  R   R  R  R  R  t(   sympy.functions.elementary.trigonometricR  R  R  R  R	  R
  R  R  R  t   it   A_t   B_t   C_Rp  t   G_t   H_Rl  Rn  t   c_Ru  t   e_t   f_t   g_t   h_t   i_t   j_t   k_t   l_Rk  Rm  Rt  t   q_t   r_t   t_Rq  Rr  Ro  Rs  Rj  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   Ct   kR5  R1  R  t	   ShowStepst   Nonet   StepCounterRö  (    (    (    sK   lib/python2.7/site-packages/sympy/integrals/rubi/rules/special_functions.pyt   <module>   s>   "˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ ˙ 1nj:R4|Ó'	