ó
¡¼™\c           @   s  d  d l  m Z m Z m Z m Z m Z m Z m Z m Z m	 Z	 m
 Z
 m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m Z m  Z  m! Z! m" Z" m# Z# 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 m Z m6 Z6 m7 Z7 m8 Z8 m9 Z9 m: Z: d  d l; m< Z< m= Z= m> Z> m? Z? m@ Z@ mA ZA d  d lB mC ZC e d ƒ \ ZD ZE ZF ZG ZH ZI ZJ ZK e# d ƒ ZL d „  ZM d „  ZN d „  ZO d	 „  ZP d
 „  ZQ d „  ZR d „  ZS d „  ZT d „  ZU d „  ZV d „  ZW d „  ZX d „  ZY d „  ZZ d „  Z[ d „  Z\ d „  Z] d „  Z^ d „  Z_ eC d „  ƒ Z` d „  Za d „  Zb eC d „  ƒ Zc d „  Zd d „  Ze d „  Zf d  „  Zg d! „  Zh eC d" „  ƒ Zi d# „  Zj d$ „  Zk d% „  Zl d& S('   iÿÿÿÿ(;   t   sint   cost   tant   sect   csct   cott   logt   expt   atant   asint   acost   Symbolt   Integralt	   integratet   pit   Dummyt
   Derivativet   difft   It   sqrtt   erft	   Piecewiset   Eqt   Net   symbolst   Rationalt   Andt	   Heavisidet   St   asinht   acosht   atanht   acotht   expandt   Functiont   jacobit
   gegenbauert
   chebyshevtt
   chebyshevut   legendret   hermitet   laguerret   assoc_laguerret
   uppergammat   lit   Eit   Cit   Sit   Chit   Shit   fresnelst   fresnelct   polylogR   t   erfit   sinht   cosht
   elliptic_ft
   elliptic_e(   t   manualintegratet   find_substitutionst   _parts_rulet   integral_stepst   contains_dont_knowt   manual_subs(   t   slows   x y z u n a b ct   fc           C   s3  t  t t ƒ d d d t t ƒ d t t ƒ d t t ƒ t t ƒ d t d d t d t d f g k sw t ‚ t  t t ƒ d t t ƒ t t ƒ t t ƒ t t ƒ t t ƒ t t ƒ t t ƒ d d t f g k sç t ‚ t  t t t d ƒ t t ƒ t d t	 j
 t t ƒ f g k s/t ‚ d  S(   Ni   i   i   i   (   R;   R   t   xR   t   ut   AssertionErrorR   R   R   R   t   Half(    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_find_substitutions   s
    =:88c           C   s|  t  t t ƒ t t k s t ‚ t  t d ƒ t ƒ t t d ƒ k sJ t ‚ t  t d t ƒ t d d k sq t ‚ t  d t d d t d t ƒ t d t d k s¬ t ‚ t  t d d t ƒ t d d d k sÛ t ‚ t  d t d d t ƒ d t d d d k st ‚ t  t d d t ƒ t d d d k sAt ‚ t  d t d d t ƒ d t d d d k sxt ‚ d  S(   Ni   i   i   i	   (   R:   t   yRB   RD   R   RC   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt    test_manualintegrate_polynomials   s    +';/7/c           C   sù   t  t d t ƒ t ƒ t d t ƒ d k s3 t ‚ t  d t t ƒ d t t d ƒ k s` t ‚ t  d t t ƒ t t ƒ k s… t ‚ t  d d t d t ƒ t d t d ƒ d k s¾ t ‚ t  t t ƒ d t t ƒ t t ƒ d d k sõ t ‚ d  S(   Ni   i   i   (   R:   R   RB   RD   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt!   test_manualintegrate_exponentials%   s
    3-%9c          C   sˆ  t  t t ƒ t t ƒ t ƒ t t ƒ t t ƒ d t t ƒ t t ƒ d k sW t ‚ t  d t t t ƒ t ƒ d t t t ƒ d t t ƒ k sœ t ‚ t  t t t ƒ t ƒ t d t t ƒ d t d d k sß t ‚ t  t t ƒ t ƒ t t t ƒ t k st ‚ t  d t d d t t ƒ t ƒ d t d t t ƒ d t t t ƒ d t t ƒ k sqt ‚ t  t t ƒ t ƒ t t t ƒ t t d d ƒ d k s²t ‚ t  t d t ƒ t d t ƒ j t	 ƒ sât ‚ t
 t t ƒ t ƒ d  k st ‚ t
 t t ƒ t ƒ d  k s$t ‚ t
 t d t ƒ d  k sCt ‚ t
 t t ƒ t ƒ }  |  d t t ƒ k r~|  d d k s„t ‚ d  S(	   Ni   i   i   i   i   i   i   i    (   R:   R   RB   R    R   RD   R   R   t   hasR   R<   t   None(   t   result(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_parts.   s    ;EC/"AA0!!c           C   s  t  t t ƒ t ƒ t t ƒ k s( t ‚ t  t t ƒ t ƒ t t t ƒ ƒ k sV t ‚ t  t t ƒ t ƒ t t t ƒ t t ƒ ƒ k s t ‚ t  t t ƒ t ƒ t t t ƒ t	 t ƒ ƒ k sÅ t ‚ t  t t ƒ t t ƒ t ƒ t t ƒ d d t t ƒ d d g k st ‚ t  t t ƒ t t ƒ t ƒ t t ƒ k sFt ‚ t  t t ƒ t	 t ƒ t ƒ t t ƒ k sxt ‚ t  t t ƒ d t ƒ t t ƒ k s£t ‚ t  t t ƒ d t ƒ t	 t ƒ k sÏt ‚ t  t t t d ƒ t ƒ t t t d ƒ t t d ƒ ƒ d k st ‚ t  t t ƒ t t t ƒ ƒ t ƒ t t	 t t ƒ ƒ t t t ƒ ƒ ƒ k snt ‚ t  t d t ƒ t t ƒ t ƒ t t d t ƒ k s¬t ‚ t  t d t ƒ t t ƒ t ƒ d t t t ƒ ƒ d t t t ƒ d ƒ d t t ƒ d k st ‚ d  S(   Ni   i   iýÿÿÿ(
   R:   R    RB   R   RD   R   R   R   R   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt!   test_manualintegrate_trigonometryC   s    (.78N32+,KT> c           C   sg  t  t t ƒ d t t ƒ t ƒ t t ƒ d d k s= t ‚ t  t t ƒ d t t ƒ d t ƒ t d t d t ƒ d k s† t ‚ t  t t ƒ t t ƒ d t ƒ t t ƒ d d k sÄ t ‚ t  t t ƒ d t t ƒ d t ƒ t t ƒ d d t t ƒ d d k st ‚ t  t t ƒ d t t ƒ t ƒ t t ƒ d d t t ƒ k s^t ‚ t  t t ƒ t t ƒ d t ƒ t t ƒ d d k s›t ‚ t  t t ƒ d t t ƒ t ƒ t t ƒ d d d t t ƒ d d t t ƒ k sùt ‚ t  t t ƒ d t t ƒ d t ƒ t t ƒ d d d t t ƒ d d t t ƒ d d k sct ‚ d  S(	   Ni   i   i   i   i    i   i   i   (	   R:   R    RB   R   RD   R   R   R   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_trigpowersW   s    =$%>$/G= >$c        
   C   se  t  t t ƒ d t d t ƒ t ƒ t t t ƒ ƒ k s? t ‚ t  d d d t d t ƒ t d t d ƒ d k s| t ‚ t  d d d t d t ƒ t t ƒ d k s± t ‚ t  d d t d t ƒ t t d ƒ d k sæ t ‚ t  d d d t d t ƒ t d t ƒ d k st ‚ t  d t t t d t ƒ t t t t t t ƒ ƒ t t t t ƒ t t d k f t	 t t t t ƒ ƒ t t t t ƒ t
 t t d k  t d t t k ƒ f t t t t t ƒ ƒ t t t t ƒ t
 t t d k  t d t t k  ƒ f ƒ k s.t ‚ t  d d t t d t ƒ t t t d t d t ƒ ƒ d t t d t ƒ d t d k f t	 t d t d	 t ƒ ƒ d t t d	 t ƒ t
 d t d k  t d d
 t k ƒ f t t d t d	 t ƒ ƒ d t t d	 t ƒ t
 d t d k  t d d
 t k  ƒ f ƒ k sOt ‚ t  d t d t d t ƒ t t d t t t ƒ ƒ d t t ƒ t d d k f t	 d t t t ƒ ƒ d t t ƒ t
 t d d k  t d t d k ƒ f t d t t t ƒ ƒ d t t ƒ t
 t d d k  t d t d k  ƒ f ƒ k sRt ‚ t  d d d t d t ƒ t t ƒ d k s‡t ‚ t  d t d t d ƒ t ƒ t t ƒ k sºt ‚ t  d t d d t d ƒ t ƒ t t ƒ d k sõt ‚ t  d t d d t d ƒ t ƒ t d t ƒ k s0t ‚ t  d t d d t d ƒ t ƒ t d t d ƒ d k sst ‚ t  d t t d d ƒ t ƒ t t ƒ k s¦t ‚ t  d t t d d ƒ t ƒ t t d ƒ k sÝt ‚ t  d t d t d d ƒ t ƒ t t ƒ d k st ‚ t  d t d t d d ƒ t ƒ t d t ƒ d k sWt ‚ t  d t t t d d ƒ t ƒ t t d	 t ƒ t t t t ƒ ƒ t d k  f t d t ƒ t t t ƒ t ƒ t d k f ƒ k sæt ‚ t  d t t t d ƒ t ƒ t t t t d t ƒ ƒ t d k f t t t d	 t ƒ ƒ t d k  f ƒ k s\t ‚ t  d t t d d ƒ t ƒ t t ƒ k st ‚ t  d t t d d ƒ t ƒ t t d ƒ k sÆt ‚ t  d t d t d d ƒ t ƒ t t ƒ d k st ‚ t  d t d t d d ƒ t ƒ t d t ƒ d k s@t ‚ t  d t t t d d ƒ t ƒ t t d t ƒ t t t ƒ t d ƒ t d k f ƒ k s¥t ‚ t  d t t d t d ƒ t ƒ t t d t t d	 t ƒ ƒ d t d k f t d t t d t ƒ ƒ d t d k  f ƒ k s2	t ‚ t  d t t t t d ƒ t ƒ t t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k  t d k ƒ f t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k t d k ƒ f t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k t d k  ƒ f ƒ k sJ
t ‚ t  d t t t t d ƒ t ƒ t t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k t d k  ƒ f t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k t d k ƒ f t t t ƒ t t t t t ƒ ƒ t t ƒ t
 t d k  t d k ƒ f ƒ k sat ‚ d  S(   Ni   i   i   i	   i   i   i   i    iÿÿÿÿiüÿÿÿ(   R:   R   RB   R   RD   t   at   bR   R   R    R   R   R	   R   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt    test_manualintegrate_inversetrigh   sl    ?=559<TcDYh8P_53;;C"""mX"""C#j"NM["OJc           C   sÞ  t  t d t d d ƒ t t ƒ t t d t d d ƒ d t d d t ƒ t t d t j d k  t d t j d k ƒ f ƒ k s t ‚ t  d t d t d t d ƒ t ƒ t t t d d d ƒ d	 t t d d d d t j	 d
 t d t t d k  t d k ƒ f ƒ k s*t ‚ t  t d d t d d d t j	 t ƒ d t d d d t j	 d d t d d d t j	 d d t d t d d ƒ d d d t d t d d ƒ k sÚt ‚ d  S(   Ni   i   i	   i   i   iýÿÿÿi   i   i}   i   i   iûÿÿÿi   i1   iÅÑ·iÁöW (
   R:   R   RB   R   R
   R   R   t   OneRD   RE   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt&   test_manualintegrate_trig_substitutionª   s    ".@&"R+c          C   s®   t  t t ƒ t t ƒ t t ƒ t t ƒ t t ƒ k sB t ‚ t d ƒ }  t  |  t ƒ |  t ƒ t t ƒ t |  t ƒ t t ƒ t |  t ƒ t t ƒ k sª t ‚ d  S(   NRA   (   R:   R   RB   R-   RD   R"   R   (   RA   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt)   test_manualintegrate_trivial_substitution¶   s    B!c           C   sÎ   t  d d t d t ƒ t t t d ƒ d t d d k f t t d ƒ d t d d k  f ƒ k sl t ‚ t  d d t d t ƒ t t t ƒ t d d k f t t ƒ t d d k  f ƒ k sÊ t ‚ d  S(   Ni   i   i   iÿÿÿÿ(   R:   RB   R   R    R   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_rational¼   s    lc          C   s}  d t  t d d ƒ d t d ƒ t t ƒ t t d ƒ t d ƒ }  } t |  t ƒ | k ry | j t ƒ j |  ƒ s t ‚ d t  d t d ƒ d t t ƒ t	 d t ƒ d }  } t |  t ƒ | k rç | j t ƒ j |  ƒ sí t ‚ t t
 d ƒ d t  t d ƒ d t t
 d ƒ d t d ƒ }  } t |  t ƒ | k r_| j t ƒ j |  ƒ set ‚ t  d t ƒ t t d t ƒ }  } t |  t ƒ | k r·| j t ƒ j |  ƒ s½t ‚ t  d d t t d ƒ t t ƒ t  d ƒ t t d ƒ d }  } t |  t ƒ | k r/| j t ƒ j |  ƒ s5t ‚ t t d d t d ƒ }  t d ƒ t t ƒ t d ƒ t t d ƒ d t d d t t ƒ ƒ t d ƒ t t d ƒ d t d d t t ƒ ƒ d } t |  t ƒ | k r| j t ƒ j |  ƒ st ‚ t d t d ƒ t d ƒ t t ƒ t d t d ƒ t t t ƒ ƒ d }  } t |  t ƒ | k r…| j t ƒ j |  ƒ s‹t ‚ t d t d ƒ t t d ƒ t d t ƒ t d ƒ t d t ƒ }  } t |  t ƒ | k r| j t ƒ j |  ƒ s	t ‚ t d t d ƒ t t d ƒ t d t ƒ t d ƒ t d t ƒ }  } t |  t ƒ | k r‚| j t ƒ j |  ƒ sˆt ‚ d t d t d ƒ t d t d ƒ t d t ƒ d t d ƒ t d t ƒ }  } t |  t ƒ | k r| j t ƒ j |  ƒ st ‚ t t d ƒ t t t d ƒ }  } t |  t ƒ | k rd| j t ƒ j |  ƒ sjt ‚ t t d ƒ t t t d ƒ d }  } t |  t ƒ | k rÀ| j t ƒ j |  ƒ sÆt ‚ d t d t d ƒ t d t d ƒ d }  } t |  t ƒ | k r$| j t ƒ j |  ƒ s*t ‚ t d d t ƒ t t d d t ƒ }  } t |  t ƒ | k r‚| j t ƒ j |  ƒ sˆt ‚ d t d d t t ƒ d ƒ d t d ƒ t t t
 d ƒ d ƒ d }  } t |  t ƒ | k r| j t ƒ j |  ƒ s	t ‚ t d d t t ƒ d ƒ d t t t
 d ƒ d ƒ }  } t |  t ƒ | k rs| j t ƒ j |  ƒ syt ‚ d  S(	   Ni   i   i   i   i   iðÿÿÿi   i	   (   R   RB   R   R   R   R:   R   t   equalsRD   R5   R   R+   R-   R    R3   R   R2   R.   R/   R6   R0   R7   R1   R   R,   R4   R8   R9   (   RA   t   F(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_specialÀ   sB    L3;3E3%3E3ƒ3Q3K3L3W3%3)313+3N3=c           C   sè   t  t t t d d t d ƒ t ƒ t t d d t d k sI t ‚ t  t t d d t d t ƒ t ƒ t t t d d t d t ƒ ƒ k sœ t ‚ t  t t t ƒ t t t t ƒ t ƒ t t t ƒ t t t ƒ k sä t ‚ d  S(   Ni   i   (   R:   R   R   RB   RD   RG   R   R    (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_derivativeå   s    &#%.$c          C   sÂ  t  t t ƒ t ƒ t t t ƒ k s+ t ‚ t  t t d ƒ t ƒ t d d k sX t ‚ t  t t d ƒ t ƒ d k s} t ‚ t  t t t ƒ t ƒ t d t t ƒ d k s´ t ‚ t  t t t ƒ t ƒ t d t t ƒ d k sí t ‚ t  t d t d ƒ t ƒ t d t d t d ƒ k s,t ‚ t  t t t ƒ t ƒ t d t t ƒ d k sct ‚ t  t t d ƒ t d t ƒ t d t ƒ t d d t d ƒ d t t d ƒ t d ƒ d t t d ƒ k sßt ‚ t d ƒ }  t  t d t ƒ t d t d ƒ t ƒ t t d ƒ t t d	 ƒ d ƒ t d t t d ƒ ƒ k sYt ‚ t  t |  t ƒ t d t |  ƒ t ƒ t d |  d ƒ t t |  ƒ t d t |  ƒ k s¾t ‚ d  S(
   Ni   iþÿÿÿi    i   i   i   RG   i   i   (   R:   R   RB   RD   R   R   R    R   (   RG   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manualintegrate_Heavisideî   s    +-%79?7,P(F(c          C   s1  t  d ƒ }  d t d ƒ d } } t |  | | t ƒ t |  | t ƒ t |  t ƒ t |  t ƒ t |  t ƒ t |  t ƒ t	 |  t ƒ t
 |  | t ƒ g } x•| D]} t | t ƒ } x d d d d d d d	 g D]d } y | j |  | ƒ } Wn t k
 rÿ qÍ n X| j |  | ƒ j t ƒ | j ƒ  d k sÍ t ‚ qÍ Wt | j t d
 t d ƒ } t | t ƒ } xT d
 d d g D]C } | j |  | ƒ j t ƒ | j |  | ƒ j ƒ  d k srt ‚ qrWt  d ƒ }	 xa t t | j ƒ d ƒ D]F }
 t | j ƒ } |	 | |
 <t t | j | Œ  |	 ƒ t ƒ sßt ‚ qßWqœ Wd  S(   Nt   ni   i   i   iþÿÿÿiÿÿÿÿi    i   i   i   i   t   t(   R   R   R#   RB   R$   R%   R&   R'   R(   R)   R*   R:   t   subst
   ValueErrorR   R!   RD   t   ranget   lent   argst   listt
   isinstancet   funcR   (   R\   RP   RQ   t   polyst   pt   integralt   degt   p_subbedt   qR]   t   it   new_args(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt$   test_manualintegrate_orthogonal_poly  s,    -0"5A 
c          C   s1  t  t d j ƒ  ƒ \ }  } } t d d t d t ƒ} t | | | ƒ t | | ƒ } | t t f } t | | ƒ | | d t d | | ƒ d t | | ƒ t | | ƒ t | | ƒ d d | k s× t ‚ |  t	 | | ƒ j
 ƒ  t |  t | | ƒ k st ‚ t	 | | ƒ j t ƒ s-t ‚ d  S(   Ns   r x phiR\   t   integert   positivei   i   (   t   mapR   t   splitt   TrueR   R   R:   R    RD   R   t   trigsimpRJ   R   (   t   rRB   t   phiR\   t	   integrandt   limits(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_6799  s    "c7c           C   sW   t  t t t ƒ t t t d t d t t d ƒ f t t ƒ t f ƒ k sS t ‚ d  S(   Ni   iÿÿÿÿ(   R:   RB   RG   R   R   R   Rs   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_12251*  s    c           C   s‘   t  t t t t d ƒ ƒ t ƒ t t t d ƒ k s= t ‚ t t t t d ƒ t d t ƒt t t	 ƒ t
 t t d ƒ d k s t ‚ d  S(   Ni   i   t   risch(   R:   R   R   RB   RD   R   t   FalseR   R   R   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_3796/  s    =c           C   sµ   t  t t ƒ t t ƒ t d t ƒt t ƒ t t ƒ d t t ƒ t t ƒ d k s] t ‚ t  t t ƒ t t ƒ t d t ƒt t ƒ d d t t ƒ d d g k s± t ‚ d  S(   Nt   manuali   (   R   R   RB   R    Rs   R   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manual_true4  s    ";"c       
   C   s¼  t  d ƒ }  t  d ƒ } t |  t t ƒ t |  t t |  ƒ t t |  ƒ d ƒ f t t f ƒ k si t ‚ t |  | t t ƒ t t |  | t t |  ƒ t t |  ƒ d ƒ f | t t f ƒ | t | d ƒ f t t f ƒ k sè t ‚ t t | t ƒ t ƒ t t | t ƒ | t | d ƒ f t t f ƒ k s9t ‚ t  d d t ƒ}  t |  d t t ƒ |  d t t |  d ƒ k s„t ‚ t  d d t ƒ}  t |  d t t ƒ t k s¹t ‚ t  d ƒ }  t  d d t ƒ} t |  | t t ƒ t |  | t t |  ƒ t t |  ƒ d ƒ f | t t f ƒ | k s8t ‚ t  d d t ƒ}  t |  d | t t ƒ |  d | t | t |  d ƒ k st ‚ t  d d	 t ƒ} t  d
 ƒ } t d | | t d t ƒ t t	 t t
 | | ƒ ƒ | t
 | | ƒ | | d k f t t t
 | | ƒ ƒ | t
 | | ƒ t | | d k  t d | | k ƒ f t t t
 | | ƒ ƒ | t
 | | ƒ t | | d k  t d | | k  ƒ f ƒ k s¼t ‚ t  d
 d	 t ƒ} t d | | t d t ƒ t	 t t
 | ƒ t
 d | ƒ ƒ | t
 | ƒ t
 d | ƒ k s5t ‚ t d t | |  | d t
 | t d d ƒ t ƒ |  | t t | |  | t
 | t d d ƒ t | t
 | t d d ƒ d t | |  | t
 | t d d ƒ t ƒ k sût ‚ t d t d d t
 d t d d ƒ t ƒ t d t d d t
 d t d d ƒ t ƒ k sct ‚ t d t | t t | d t ƒ t d | t | d t t t ƒ k s¸t ‚ d  S(   NRG   R\   i    Rp   i   t   zerot   nonzeroRP   t   negativeRQ   i   iÿÿÿÿi   (   R   R:   RB   R   R   R   Rs   RD   R   R   R   R    R   R   R   (   RG   R\   RP   RQ   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_6746;  sN    >*89#J-<TcK6}.:$c           C   sÉ  t  t t ƒ t t ƒ t ƒ t t t ƒ t t d d ƒ t t t ƒ t t d d ƒ t t ƒ t t t d d ƒ t t ƒ k s” t ‚ t  t t ƒ t t ƒ t ƒ t t t ƒ t t d d ƒ t t t ƒ t t d d ƒ t t ƒ t t t d d ƒ t t ƒ k s(t ‚ t  t t ƒ t t ƒ t ƒ t t t ƒ t t t ƒ t t d d ƒ d t t ƒ t t d d ƒ d t t t d d ƒ t t ƒ d k sÅt ‚ d  S(   Ni   i   (	   R:   R	   RB   R   R   R   RD   R
   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_2850f  s    xxc        	   C   sD  t  t d t ƒ t t ƒ t ƒ t t ƒ t d t ƒ d d t t ƒ t d t ƒ d k sg t ‚ t t t d t ƒ t t ƒ t ƒ ƒ s— t ‚ t  t d t d d t d d t ƒ t t t d d t d d t d d t d t ƒ d t d t d d t d d t d d t d t ƒ k s@t ‚ d  S(   Ni   i   i   i   i   i   (	   R:   R    RB   R   R   RD   R>   R=   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_9462o  s
    g0(8c          C   sd  t  t ƒ t t d ƒ }  d t t d ƒ t t ƒ d d t t d ƒ t  t ƒ d } t |  t ƒ | k r† | j t ƒ |  k sŒ t ‚ t t  t ƒ t t d ƒ }  t d t t d ƒ t t ƒ d d t t d ƒ t  t ƒ d d t t d ƒ t t ƒ d d t t d ƒ t  t ƒ d } t |  t ƒ | k rZ| j t ƒ |  k s`t ‚ d  S(   Ni   i   i   i€   i!  ið   (   R   RB   R   R    R:   R   RD   (   RA   RX   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_cyclic_partsw  s    B0†c           C   s{	  t  t d t d t t ƒ t t t t t t ƒ ƒ t t ƒ t d k f t t t t ƒ ƒ t t ƒ t t d k  t d t k ƒ f t t t t ƒ ƒ t t ƒ t t d k  t d t k  ƒ f ƒ t k sÞ t	 ‚ t  t t t
 ƒ t t t ƒ t ƒ d t
 d t t t t t
 ƒ t t
 ƒ ƒ t t
 ƒ t
 d k f t t t t
 ƒ t t
 ƒ ƒ t t
 ƒ t t t
 t
 k t
 d k  ƒ f t t t t
 ƒ t t
 ƒ ƒ t t
 ƒ t t t
 t
 k  t
 d k  ƒ f ƒ d d t
 t t t
 ƒ d d t t
 t d ƒ d t t t ƒ d d t t
 t d ƒ d d k sOt	 ‚ t  t t ƒ t t ƒ t ƒ d t t d ƒ d t t ƒ d d t t d ƒ d d k s´t	 ‚ t  t t t t ƒ t t ƒ d t t t t t t t ƒ t t ƒ ƒ t t ƒ t d k f t t t t t ƒ t t ƒ ƒ t t ƒ t t d k  t t t t k ƒ f t t t t t ƒ t t ƒ ƒ t t ƒ t t d k  t t t t k  ƒ f ƒ d t t t t ƒ k sÛt	 ‚ t t  t t t t ƒ t t t ƒ ƒ d t t t t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t d k f t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t t d k  t t t t t t k ƒ f t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t t d k  t t t t t t k  ƒ f ƒ d t t t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t d k f t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t t d k  t t t t t t k ƒ f t t t t t ƒ t t t t ƒ ƒ t t t t ƒ t t t t d k  t t t t t t k  ƒ f ƒ d t t t t ƒ k s¬t	 ‚ t  d t d d t d d t d d t d	 t d
 d t d d t d d t d d t d d t d t ƒ d t t d d d t t ƒ d t d d d t d k sqt	 ‚ t  t d t d ƒ t d t ƒ d t d t d ƒ t t d t d ƒ d ƒ t t d t d ƒ d ƒ k sìt	 ‚ t  t d t d ƒ d t t ƒ d t d t d ƒ d d d t d t d ƒ d d k sUt	 ‚ t  t t d d ƒ t t ƒ t ƒ d t t d d ƒ t t ƒ d d t t d d ƒ d k s¿t	 ‚ t  t d t t ƒ t ƒ t t ƒ d t d d d t d k s	t	 ‚ t  t t
 ƒ t
 d d d t
 t
 ƒ t t
 ƒ t d d t
 ƒ t t d d t
 ƒ t
 t
 ƒ k sw	t	 ‚ d  S(   Ni   i    i   i   i	   iþÿÿÿi   i   i   i   i   i   i   i   iýÿÿÿiÿÿÿÿ(   R:   RB   t   cR   R   R   R    R   R   RD   RG   R   t   zR   RP   RQ   R!   R   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_10847  s0    N>R$ÿ NecOS"(ÿ ÿ «2JI{ijL&c           C   s”   t  t t t ƒ j t ƒ t ƒ t t t t t ƒ t ƒ t ƒ k sH t ‚ t  t t t ƒ j t ƒ j t ƒ t ƒ t t t t ƒ t ƒ k s t ‚ d  S(   N(   R:   RA   RB   RG   R   R   R   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_12899¥  s    Hc           C   sG   t  t t t d d f ƒ t ƒ t t t t d d f ƒ k sC t ‚ d  S(   Ni   i   (   R:   R   RG   RB   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt#   test_constant_independent_of_symbolª  s    c           C   sæ   t  t d t ƒ t ƒ t d t ƒ d k s4 t ‚ t  t t ƒ t d t ƒ t ƒ d t t ƒ d d k su t ‚ t  t d t ƒ t t ƒ d t t ƒ t ƒ d t t t ƒ d ƒ t t ƒ d d t t ƒ k sâ t ‚ d  S(   Ni   iþÿÿÿi   i   (   R:   R    RB   R   RD   R   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_12641¯  s    4A.c           C   sB   t  t t ƒ t t ƒ d t ƒ t t ƒ d d k s> t ‚ d  S(   Ni   i   (   R:   R    RB   R   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_13297¶  s    c           C   se   t  d t t t d ƒ t ƒ t d d t t d ƒ ƒ t d d t t d ƒ ƒ k sa t ‚ d  S(   Ni   iÿÿÿÿ(   R:   RB   R   R   RD   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_14470¹  s    c          C   s_  t  t t ƒ t t t ƒ ƒ t ƒ t t t ƒ ƒ k s= t ‚ t  t d t ƒ t t t ƒ ƒ t ƒ t t ƒ t t t ƒ ƒ t t t ƒ ƒ k s˜ t ‚ t  t d t ƒ t t t ƒ ƒ t ƒ }  |  j t ƒ s× t ‚ |  j t ƒ t d t ƒ t t t ƒ ƒ k st ‚ t  t	 g  t
 d d ƒ D] } t t | t ƒ ^ q"ƒ t ƒ t t d t ƒ d t t d t ƒ d t t d t ƒ d t t d t ƒ d t t d	 t ƒ d	 t t d t ƒ d t t t ƒ t d t ƒ d
 t d t ƒ d t d t ƒ d t d t ƒ d t d	 t ƒ d t d t ƒ d t t ƒ k s[t ‚ d  S(   Ni   i
   i   i   i   i   i   i   i   i1   i$   i   i   i	   (   R:   R   RB   R   R    RD   RJ   R   R   t   sumR`   (   t   rest   k(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_9858¾  s    =&5)5<c          C   sº   t  t t d d t ƒ t t d ƒ d k s5 t ‚ t  t d t d d t ƒ t t d d ƒ d k sr t ‚ t d	 t d d d }  t  |  t ƒ j t ƒ j ƒ  |  k s¶ t ‚ d  S(
   Ni   i   i   i   i   i   i   i   i	   (   R:   RB   R   RD   R   t   factor(   RA   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_8520Í  s    5=c          C   sŽ   t  d ƒ \ }  } t |  ƒ t |  ƒ } t | t |  ƒ | ƒ | t t | ƒ ƒ k s\ t ‚ t | t |  ƒ | ƒ t |  ƒ | k sŠ t ‚ d  S(   Ns   x y(   R   R   R   R?   RD   (   RB   RG   t   expr(    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_manual_subsÔ  s    4c          C   s  t  t ƒ t t  t ƒ ƒ t t d ƒ d }  d t t d ƒ d t t  t ƒ ƒ d d t t d ƒ d t t  t ƒ ƒ d d t t d ƒ d t t  t ƒ ƒ d d t t d ƒ d t t  t ƒ ƒ d t  t ƒ } t |  t ƒ | k r| j t ƒ j |  ƒ st ‚ d  S(	   Ni   i   i€ÿÿÿi   i!  ið   i   i   (	   R   RB   R   R   R    R:   R   RW   RD   (   RA   RX   (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   test_issue_15471Ý  s    .´N(m   t   sympyR    R   R   R   R   R   R   R   R   R	   R
   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R   R    R!   R"   R#   R$   R%   R&   R'   R(   R)   R*   R+   R,   R-   R.   R/   R0   R1   R2   R3   R4   R5   R6   R7   R8   R9   t   sympy.integrals.manualintegrateR:   R;   R<   R=   R>   R?   t   sympy.utilities.pytestR@   RB   RG   Rˆ   RC   R\   RP   RQ   R‡   RA   RF   RH   RI   RM   RN   RO   RR   RT   RU   RV   RY   RZ   R[   Rn   Ry   Rz   R}   R   Rƒ   R„   R…   R†   R‰   RŠ   R‹   RŒ   R   RŽ   R’   R”   R–   R—   (    (    (    s@   lib/python2.7/site-packages/sympy/integrals/tests/test_manual.pyt   <module>   sJ   ÿ m.$								B				%									+			
$								