
    \h              
       r   S SK Jr  S SKJr  S SKJrJrJrJr  S SK	J
r
JrJr  S SKJr  S SKJr  S SKJrJrJr  S SKJrJr  S S	KJrJrJrJrJrJrJr  S S
K J!r!  S SK"J#r#J$r$  S SK%J&r&J'r'J(r(J)r)J*r*J+r+J,r,J-r-J.r.J/r/J0r0J1r1  S SK2J3r3J4r4  S SK5J6r6J7r7  S SK8J9r9J:r:J;r;J<r<J=r=J>r>J?r?J@r@JArAJBrB  S SKCJDrD  S SKEJFrFJGrGJHrHJIrIJJrJJKrKJLrLJMrM  S SKNJOrO  S SKPJQrQJRrR  S SKSJTrT  S SKUJVrVJWrWJXrXJYrYJZrZ  S SK[J\r\J]r]  \" S5      u
  r^r_r`rarbrcrdrerfrg\" S5      rhS\S\4S jriS rjS rkS rlS rmS rn\]S  5       ro\]S! 5       rpS" rqS# rrS$ rsS% rtS& ruS' rvS( rw\]S) 5       rxS* ryS+ rzS, r{S- r|\]S. 5       r}S/ r~S0 r\]S1 5       r\]S2 5       rS3 rS4 rS5 r\]S6 5       rS7 r\]S8 5       rS9 rS: r\]S; 5       rS< rS= rS> rS? rS@ rSA rSB rSC rSD rgE)F    )Expr)Mul)
DerivativeFunctiondiffexpand)IRationalpi)Ne)S)DummySymbolsymbols)explog)asinhcschcoshcothsechsinhtanh)sqrt)	Piecewisepiecewise_fold)acosacotacscasecasinatancoscotcscsecsintan)	Heaviside
DiracDelta)
elliptic_e
elliptic_f)
ChiCiEiShiSierferfifresnelcfresnelsli)
uppergamma)assoc_laguerre
chebyshevt
chebyshevu
gegenbauerhermitejacobilaguerrelegendre)polylog)Integral	integrate)And)manualintegratefind_substitutions_parts_ruleintegral_stepsmanual_subs)raisesslowzx y z u n a b c d efFc                     [        U [        5      U:X  d   eUR                  [        5      R                  U 5      (       d   eg N)rD   xr   equalsrK   rL   s     Y/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_manual.pyassert_is_integral_ofrS      s6    1a A%%%66!9A    c                  V   [        [        [        5      S-  S-   S-  [        [        5      S-  -  [        [        5      S-  -  [        [        5      [        [        5      S[        S-  * S[        S-  -  -
  [        S-  -
  4/:X  d   e[        [        [        5      S-  [        [        5      [        [        5      -  -   [        [        5      [        [        5      -   -  [        [        5      [        [        5      [        [        5      -   SS[        -  4/:X  d   e[        S-  * [        SS5      [        [        5      4[        [        [        [        S-  * 5      -  [        [        5      ;   d   e[        [        [        [        5      [        5      S-  [        [        5      (       a   eg )N            )rE   r$   rO   r%   ur&   r(   r
   r   r   rK    rT   rR   test_find_substitutionsr]   "   sC   s1vqy1}q0Q:3q619DaK
a&!adUQq!tV^ad*	+,- - -s1vqy3q6CF?:s1vAO$),Q#a&!QqS(A'BC C CTE8B?CF+/A!c1a4%j.RSUV/WWWW!*QqT1"5q"8!Q?????rT   c                     [        [        [        5      [        [        -  :X  d   e[        [        S5      [        5      [        [        S5      -  :X  d   e[        [        S-  [        5      [        S-  S-  :X  d   e[        S[        S-  -  S[        S-  -  -   [        5      [        S-  [        S-  -   :X  d   e[        [        S-   S-  [        5      [        S-   S-  S-  :X  d   e[        S[        -  S-   S-  [        5      S[        -  S-   S-  S-  :X  d   e[        [        S-   S-  [        5      [        S-   S-  S-  :X  d   e[        S[        -  S-   S-  [        5      S[        -  S-   S-  S-  :X  d   eg )NrV      rY   	   )rD   yrO   r   r[   r\   rT   rR    test_manualintegrate_polynomialsrb   +   sI   1a AaC'''3q61%SV3331a4#q!tax///1q!t8a!Q$h.2adQTkAAAAEA:q)a!eaZ!^;;;AaC!Ga<+!a!|a/????AEA:q)a!eaZ!^;;;AaC!Ga<+!a!|a/????rT   c                     [        [        S[        -  5      [        5      [        S[        -  5      S-  :X  d   e[        S[        -  [        5      S[        -  [        S5      -  :X  d   e[	        S[        S[        S[        -  5      -
  5      -  [        [        S[        S[        -  5      -
  5      S-
  5      S-  [        [        S[        S[        -  5      -
  5      S-   5      S-  -
  5        [        S[        -  [        5      [        [        5      :X  d   e[        SS[        -  S-   -  [        5      [        S[        -  S-   5      S-  :X  d   e[        [        [        5      S-  [        -  [        5      [        [        5      S-  S-  :X  d   e[	        [        [        -  [        [        5      S-   -  [        [        -  5        g )NrV   rW   r_   )rD   r   rO   r   rS   r   r\   rT   rR   !test_manualintegrate_exponentialsrd   8   sX   3qs8Q'3qs8a<7771a4#Q#a&'8888!D3qs8,,d1s1Q3x<0145a7#d1s1Q3x<>PST>T:UVW:WWY 1q5!$A...1!a=!,AaC!Gq0@@@@3q619q=!,A	A===!Q$Aq/1a40rT   c                     [        [        [        5      [        [        5      -  [        5      [        [        5      [        [        5      -  S-  [        [        5      [	        [        5      -  S-  -
  :X  d   e[        S[        -  [	        [        5      -  [        5      S[        -  [        [        5      -  S[	        [        5      -  -   :X  d   e[        [        [        [        5      -  [        5      [        S-  [        [        5      -  S-  [        S-  S-  -
  :X  d   e[        [        [        5      [        5      [        [        [        5      -  [        -
  :X  d   e[        S[        S-  -  S-   [        [        5      -  [        5      S[        S-  -  [        [        5      -  S[        -  [        [        5      -  -
  S[        [        5      -  -   :X  d   e[        [        [        5      [        5      [        [        [        5      -  [        [        S-  S-   5      S-  -
  :X  d   e[        [	        [        5      [        5      S :X  d   e[        [        [        5      [        5      S :X  d   e[        [        S-  [        5      S :X  d   e[        [        [        5      [        5      n U S   [        [        5      :X  a	  U S   S:X  d   eg )	NrV   rY   r_      rX      rW   r   )rD   r   rO   r'   r#   r   r"   rF   )results    rR   test_manualintegrate_partsri   E   s   3q6CF?A.	Q#a&AQ#a&A 556 6 61Q3s1v:q)QqSQZ!CF(-BBBB1s1v:q)QT#a&[]QT!V-CCCC3q61%SVa777AadFQJ#a&0!4	!Q$s1v!CF
"RAY./ / /47A&!DG)c!Q$(mAo*EEEE s1vq!T)))s1vq!T)))q!tQ4'''a!$F!9QF1IN22NrT   c            	      V   [        [        [        5      [        5      [        [        5      * :X  d   e[        [	        [        5      [        5      [        [        [        5      5      * :X  d   e[        [        [        5      [        5      [        [        [        5      [	        [        5      -   5      :X  d   e[        [        [        5      [        5      [        [        [        5      [        [        5      -   5      * :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      S-  S-  [        [        5      S-  * S-  4;   d   e[        [        [        5      * [	        [        5      -  [        5      [        [        5      * :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      * :X  d   e[        [        [        5      S-  [        5      [	        [        5      :X  d   e[        [        [        5      S-  [        5      [        [        5      * :X  d   e[        [        [        [        S-  5      -  [        5      [        [	        [        S-  5      [        [        S-  5      -   5      S-  :X  d   e[        [        [        5      [        [        [        5      5      -  [        5      [        [        [        [        5      5      [        [        [        5      5      -   5      * :X  d   e[        [        S[        -  5      [        [        5      -  [        5      [        * [        S[        -  5      -   :X  d   e[        [        S[        -  5      [        [        5      -  [        5      S[        [        [        5      5      -  S[        [        [        5      S-  5      -  -   S[        [        5      S-  -  -
  :X  d   e[        [        S[        -  5      [        S[        -  5      S-  5        [        [        [        [        S-  5      -  [        [        S-  5      S-  5        [        [        [        5      [        [        [        5      5      5        [        [        [        5      [        [        [        5      5      5        [        [        5      S[        [        [        S-  5      5      -  p[        U [        5      U:X  d   eUR!                  [        5      U -
  R#                  [$        5      R'                  5       S:X  d   e[)        [        5      [        [        [        S-  5      5      p[        U [        5      U:X  d   eUR!                  [        5      U -
  R#                  [$        5      R'                  5       S:X  d   eg )NrV   r_   r   )rD   r'   rO   r#   r(   r   r&   r%   r$   rS   r   r   r   r   r   r"   r   rewriter   simplifyr   rQ   s     rR   !test_manualintegrate_trigonometryrn   X   s   3q61%#a&0003q61%#c!f+5553q61%SVc!f_)====3q61%#c!fs1vo*>)>>>>3q6CF?A.3q6Q;?SVQYJQRN2SSSSCF7SV+Q/CF7:::3q6CF?A.3q6'9993q619a(CF2223q619a(SVG3331s1a4y=!,C1IAqD	4I0J10LLLL3q6#c!f+-q1c#c!f+CPQF:S6T5TTTT3qs8CF?A.1"s1Q3x-???3qs8CF?A.
3s1v;3s1vqy>))Ac!faiK78 8 8 $qs)T!A#Yq[1!DAJ,QT
15$q'3tAw<0$q'3tAw<07Ad4!9o%q1a A%%%FF1IM""3'002a7777CQqS	Nq1a A%%%FF1IM""3'002a777rT   c                     [        [        [        5      S-  [        [        5      -  [        5      [        [        5      S-  S-  :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        S-  [        S[        -  5      S-  -
  :X  d   e[        [        [        5      [        [        5      S-  -  [        5      [        [        5      S-  * S-  :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        [        5      S-  S-  [        [        5      S-  S-  -
  :X  d   e[        [	        [        5      S-  [        [        5      -  [        5      [        [        5      S-  S-  [        [        5      -
  :X  d   e[        [	        [        5      [        [        5      S-  -  [        5      [        [        5      S-  S-  :X  d   e[        [        [        5      S-  [        [        5      -  [        5      [        [        5      S-  * S-  S[        [        5      S-  -  S-  -   [        [        5      -
  :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        [        5      S-  * S-  S[        [        5      S-  -  S-  -
  [        [        5      S-  S-  -
  :X  d   eg )	NrV   r_      rY       rf   rX      )rD   r'   rO   r#   r(   r&   r$   r%   r\   rT   rR   test_manualintegrate_trigpowersrs   w   s)   3q619s1v-q1SVQY]BBB3q619s1vz115	AAaC2  3q6CFAI-q1c!faiZ!^CCC3q619s1vqy0!4A	AA	A%& & & 3q619s1v-q1SVQYq[3q65IIII3q6CFQJ.2c!faikAAA3q619s1v-q1	Q
1qQ{1}$s1v-. . .3q619s1vqy0!4	Q
1qQ{1}$s1vqy{23 3 3rT   c                  ,   [        [        [        5      S[        S[        -  5      -   -  [        5      [        [        [        5      5      :X  d   e[        SSS[        S-  -  -   -  [        5      [        S[        -  S-  5      S-  :X  d   e[        SSS[        S-  -  -   -  [        5      [        [        5      S-  :X  d   e[        SS[        S-  -   -  [        5      [        [        S-  5      S-  :X  d   e[        SSS[        S-  -  -   -  [        5      [        S[        -  5      S-  :X  d   e[	        SS	S
9n [	        SS	S
9n[        SX[        S-  -  -   -  [        5      [        [        [        [        X-  5      -  5      U[        X-  5      -  -  X-  S:  4[        [        [        U * U-  5      -
  5      [        [        [        U * U-  5      -   5      -
  S[        U5      -  [        U * 5      -  -  S	45      :X  d   e[        SSU[        S-  -  -   -  [        5      [        [        [        S[        SU-  5      -  -  5      SU-  [        SU-  5      -  -  SU-  S:  4[        * [        [        S[        SU-  5      -  -
  5      [        [        S[        SU-  5      -  -   5      -
  -  S[        U5      -  -  S	45      :X  d   e[        SU S[        S-  -  -   -  [        5      [        [        S[        -  [        U 5      -  5      S[        U 5      -  -  U S:  4[        [        [        U * 5      S-  -
  5      [        [        [        U * 5      S-  -   5      -
  S[        U * 5      -  -  S	45      :X  d   e[        SSS[        S-  -  -   -  [        5      [        [        5      S-  :X  d   e[        S[        [        [        S-  -  -   -  [        5      [        [        [        [        [        [        -  5      -  5      [        [        [        [        -  5      -  -  [        [        S5      4S[        [        -  -  S	45      :X  d   e[        S[        S[        S-  -
  5      -  [        5      [        [        5      :X  d   e[        S[        SS[        S-  -  -
  5      -  [        5      [        [        5      S-  :X  d   e[        S[        SS[        S-  -  -
  5      -  [        5      [        S[        -  5      :X  d   e[        S[        SS[        S-  -  -
  5      -  [        5      [        [        [        SS5      -  5      S-  :X  d   e[        S[        [        S-  S-   5      -  [        5      [        [        5      :X  d   e[        S[        [        S-  S-   5      -  [        5      [        [        S-  5      :X  d   e[        S[        S[        S-  -  S-   5      -  [        5      [        [        5      S-  :X  d   e[        S[        S[        S-  -  S-   5      -  [        5      [        S[        -  5      S-  :X  d   e[        S[        U [        S-  -  S-   5      -  [        5      [        [        [        [        U * 5      -  5      [        U * 5      -  U S:  4[        [        U 5      [        -  5      [        U 5      -  U S:  4[        S	45      :X  d   e[        S[        U [        S-  -   5      -  [        5      [        [        [        [        SU -  5      -  5      U S:  4[        S[        -  S[        U [        S-  -   5      -  -   5      S	45      :X  d   e[        S[        [        S-  S-
  5      -  [        5      [        S[        -  S[        [        S-  S-
  5      -  -   5      :X  d   e[        S[        [        S-  S-
  5      -  [        5      [        S[        -  S[        [        S-  S-
  5      -  -   5      :X  d   e[        S[        S[        S-  -  S-
  5      -  [        5      [        S[        -  S[        S[        S-  -  S-
  5      -  -   5      S-  :X  d   e[        S[        S[        S-  -  S-
  5      -  [        5      [        S[        -  S[        S[        S-  -  S-
  5      -  -   5      S-  :X  d   e[        S[        U [        S-  -  S-
  5      -  [        5      [        [        S[        U 5      -  [        U [        S-  -  S-
  5      -  SU -  [        -  -   5      [        U 5      -  [        U S5      4[        * [        -  S-  S	45      :X  d   e[        S[        U * S[        S-  -  -   5      -  [        5      [        [        S[        -  [        SU -  5      -  5      S-  U S:  4[        S[        -  S[        U * S[        S-  -  -   5      -  -   5      S-  S	45      :X  d   e[        [        [        5      [        5      [        [        [        5      -  [        S[        S-  -
  5      -   :X  d   e[        [        [        [        -  5      [        5      [        [        [        -  [        [        [        -  5      -  [        [        S-  * [        S-  -  S-   5      -   [        -  [        [        S5      4S5      :X  d   e[        [        [        [        [        -  5      -  [        5      [        * [        [        * [        [        S-  * [        S-  -  S-   5      -  S[        S-  -  -  [        S[        S-  -  [        -  S[        [        S-  * 5      -  [        [        S-  * [        S-  -  S-   5      -  -   5      S[        S-  -  [        [        S-  * 5      -  -  -   [        [        S-  S5      4[        S-  S-  S	45      -  S-  [        S-  [        [        [        -  5      -  S-  -   :X  d   e[        [        [        5      [        5      [        [        [        5      -  [        S[        S-  -
  5      -
  :X  d   e[        [        [        [        -  5      [        5      [        [        [        -  [        [        [        -  5      -  [        [        S-  * [        S-  -  S-   5      -
  [        -  [        [        S5      4[         [        -  S-  S	45      :X  d   e[        [        [        [        [        -  5      -  [        5      [        [        [        * [        [        S-  * [        S-  -  S-   5      -  S[        S-  -  -  [        S[        S-  -  [        -  S[        [        S-  * 5      -  [        [        S-  * [        S-  -  S-   5      -  -   5      S[        S-  -  [        [        S-  * 5      -  -  -   [        [        S-  S5      4[        S-  S-  S	45      -  S-  [        S-  [        [        [        -  5      -  S-  -   :X  d   e[        [        [        5      [        5      [        [        [        5      -  [        [        S-  S-   5      S-  -
  :X  d   e[        [        [        [        -  5      [        5      [        [        [        -  [        [        [        -  5      -  [        [        S-  [        S-  -  S-   5      S-  -
  [        -  [        [        S5      4S5      :X  d   e[        [        [        [        [        -  5      -  [        5      [        * [        [        S-  -  [        [        [        [        S-  5      -  5      [        S-  [        [        S-  5      -  -  -
  -  S-  [        S-  [        [        [        -  5      -  S-  -   :X  d   e[        [#        [        5      [        5      [        [#        [        5      -  [%        S[        [        SS[        S-  -  -
  5      -  -  [        5      -   :X  d   e[        [#        [        [        -  5      [        5      [        [#        [        [        -  5      -  [%        S[        [        SS[        S-  [        S-  -  -  -
  5      -  -  [        5      [        -  -   :X  d   e[        [        [#        [        [        -  5      -  [        5      [        S-  [#        [        [        -  5      -  S-  [%        S[        SS[        S-  [        S-  -  -  -
  5      -  [        5      S[        -  -  -   :X  d   e[        ['        [        5      [        5      [        ['        [        5      -  [%        S[        [        SS[        S-  -  -
  5      -  -  [        5      -
  :X  d   e[        ['        [        [        -  5      [        5      [        ['        [        [        -  5      -  [%        S[        [        SS[        S-  [        S-  -  -  -
  5      -  -  [        5      [        -  -
  :X  d   e[        [        ['        [        [        -  5      -  [        5      [        S-  ['        [        [        -  5      -  S-  [%        S[        SS[        S-  [        S-  -  -  -
  5      -  [        5      S[        -  -  -
  :X  d   e[        [)        [        5      [        5      [        [)        [        5      -  [        [        S-  S-   5      S-  -   :X  d   e[        [)        [        [        -  5      [        5      [        [        [        -  [)        [        [        -  5      -  [        [        S-  [        S-  -  S-   5      S-  -   [        -  [        [        S5      4[         [        -  S-  S	45      :X  d   e[        [        [)        [        [        -  5      -  [        5      [        [        [        S-  -  [        [        [        [        S-  5      -  5      [        S-  [        [        S-  5      -  -  -
  -  S-  [        S-  [)        [        [        -  5      -  S-  -   :X  d   e[        S[        X[        S-  -  -
  5      -  [        5      [        [        [        [        X-  5      -  5      [        U5      -  [+        U* S:  U S:  5      4[        [        [        U* U -  5      -  5      [        U* 5      -  [+        U* S:  U S:  5      4[        SU-  [        -  S[        U* 5      -  [        X[        S-  -  -
  5      -  -   5      [        U* 5      -  [        US5      4[        [        U 5      -  S	45      :X  d   e[        S[        X[        S-  -  -   5      -  [        5      [        [        [        [        U* U -  5      -  5      [        U* 5      -  [+        U S:  US:  5      4[        [        [        X-  5      -  5      [        U5      -  [+        U S:  US:  5      4[        S[        U5      -  [        X[        S-  -  -   5      -  SU-  [        -  -   5      [        U5      -  [        US5      4[        [        U 5      -  S	45      :X  d   eg )NrW   rV   rY   r`   r_   rX      aTrealbr   rZ   rp      )r   T)rD   r   rO   r"   r   r   r   r   r	   rv   ry   r   r!   r
   r   r   r   r   rA   r    r   rC   )rarbs     rR    test_manualintegrate_inversetrigr~      s    3q6QQqS\2A6$s1v,FFF1A1H-q1T!a%']Q5FFFF1R!Q$Y/3tAw|CCC1AqD>1-a!eq@@@1A1H-q1T!A#Y]BBB	$	B	$	B1bad7l+Q/4$ru+&4;7CD"RL()CD"RL0@,AAAd2hJtUWTWyDXY[_`	bb b b 1a"QT'k?A.41T!B$Z<()1R4QrT
?;QrTAXF2s1qbe},-A$r"u+4E0FFG4PR8TVZ[	]] ] ] 1b1QT6k?A.4!DH%qbz2BF;D"IaK(3q49Q;+??!D"I+NPTU	WW W W 1a!AqD&j>1-a1<<<1a!AqD&j>1-D4!9<MqQUVWXYVYQZ{<[]_`acd]e;f<>!Hd;K2M M M M 1T!AqD&\>1-a8881T!AadF(^+Q/4719<<<1T!AadF(^+Q/4!9<<<1T!AadF(^+Q/4(1a.8H3I!3KKKK 1T!Q$(^+Q/a  1T!Q$(^+Q/ac
  1T!AqD&1*--q1a
  1T!AqD&1*--q1ac
1  1T"QT'A+..24$s)$T2#Y.Q7%R
:KDQSH:TVX[\V\9]`acg_hij j j1T"q!t)_,a054":&Q/#acAd219o<M6M2NPT1UVW W W 1T!Q$(^+Q/3qsQtAqD1H~=M7M3NNNN1T!Q$(^+Q/3qsQtAqD1H~=M7M3NNNN1T!AqD&1*--q1S1qa1fqjAQ?Q9Q5RST5TTTT1T!AqD&1*--q1SA$qAvPQzBR@R9R5STU5UUUU1T"QT'A+..2c!DH*T"QT'A+%662a?@bI2bRS9UYZXZ[\X\]^X^`dWefg g g1T2#!Q$,//351T"R%[)!+R!V4s1Q34aPQSTPTfCUAU;U7VWX7XZ^6_`a a a
 47A&!DG)d1q!t8n*DDDD4!9a(I!D1IaQRdUSTVWSWZZ[^H\8\^_7_acdeghai6jlu,vvvv1T!A#Y;*2i!D!Q$q!ta00!AqD&9R1WQY4A;tQTE!Q$JN7K)KKLaPQSTPTfUY[\^_[_Z_U`N`abcefgijfjlmcnpAa( (()*,-qDacN1,<== = =
 47A&!DG)d1q!t8n*DDDD4!9a(I!D1IaQRdUSTVWSWZZ[^H\8\^_7_acdeghai6jmopqmqrsmsuylz,{{{{1T!A#Y;*Y4Aad
Q//1a48Bq!tGAI$1u+dAqD5A:>6J(JJKQqRStVTXZ[]^Z^Y^T_M_`abdefhieiklbmo1Q~' ''()+,a4QqS	>!+;<< < <
 47A&!DG)c!Q$(mAo*EEEE4!9a(I!D1IAqDQRTUQUIXYMHZ[\H\8\^_7_acdeghai6jlu,vvvv1T!A#Y;*qb!AqD&4$q2w-;PRSUVRVW[\]`b\cWdRd;e2e.fgh.hklnokoptuvwxuxpykyz{k{.{{{{47A&!DG)hq!DQqRStVDTBT?UWX6Y*YYYY4!9a(Ad1Q3iK(1aQQRTUWXTXYZ\]Y]T]Q^M^H_F_C`bc:def:f,ffff1T!A#Y;*ad4!9nQ.>!DQRUVXY[\X\]^`a]aXaUbQbLcJcefAgijklilAm.mmmm47A&!DG)hq!DQqRStVDTBT?UWX6Y*YYYY4!9a(Ad1Q3iK(1aQQRTUWXTXYZ\]Y]T]Q^M^H_F_C`bc:def:f,ffff1T!A#Y;*ad4!9nQ.>!DQRUVXY[\X\]^`a]aXaUbQbLcJcefAgijklilAm.mmmm47A&!DG)c!Q$(mAo*EEEE4!9a(I!D1IAqDQRTUQUIXYMHZ[\H\8\^_7_acdeghai6jmopqmqrsmsuylz,{{{{1T!A#Y;*a1a4$qa"g:OQRTUQUVZ[\_a[bVcQc:d1d.efg.gjkmnjnostuvwtwoxjxyzjz.zzzz 1T"1W*--q14$ru+&tBx/bS1Wb1f1EF4B<(rc2Caa4HIr"uQw49T"!Q$w,-?!??@rcJBrSTIVT"X:t$	&& & &
 1T"!Q$w,//34$s2v,'bS	13rAvrAv3FG4;'R0#b1fb1f2EFqbz$rq!tG|"44qtAv=>tBxGBPQST"X:t$	&& & &rT   c                  $   [        [        S[        S-  -  S-
  5      [        -  [        5      [        [        S[        S-  -  S-
  5      S[	        SS[        -  -  5      -  -
  [        [        [        SS5      :  [        [        SS5      :  5      45      :X  d   e[        S[        S-  [        S[        S-  -
  5      -  -  [        5      [        [        [        S-  * S-  S-   5      * S	[        -  -  [        S-  * S-  S-   S[        R                  -  -  S
[        S-  -  -  -
  [        [        S:  [        S:  5      45      :X  d   e[        [        S-  S[        S-  -  S-   S[        R                  -  -  -  [        5      S[        S-  -  S-   S[        R                  -  -  S-  S[        S-  -  S-   S[        R                  -  -  S-  -
  S[        S[        S-  -  S-   5      -  S-  -   SS[        S[        S-  -  S-   5      -  -  -   :X  d   eg )Nru   rV   r`   r_   rY   rk   rW      }      rf   rr   1   iѷiW )	rD   r   rO   r   r   rC   r
   r   Halfr\   rT   rR   &test_manualintegrate_trig_substitutionr      s   41a4!,Q.241a4!$qa1g6q8Aq>)1xA+>?A 	BB B B 1adT"QT']23Q7D!Q$rA&&A.TE"HqLAaffH-r!Q$w789<QUAF9KM 	NN N N 1a4AqD1AFF
 ;;Q?
QT'A+166	"8	+
QT'A+166	"7	*
+	
41a4!	W	$
%'('$r!Q$w{2C*C'D
EF F FrT   c                     [        [        [        5      [        [        * 5      -
  [        -  [        5      [        [        * 5      * [        [        5      -   :X  d   e[	        S5      n [        U " [        5      U " [        * 5      -
  [        -  [        5      [        U " [        * 5      [        -  [        5      * [        U " [        5      [        -  [        5      -   :X  d   eg )NrK   )rD   r   rO   r/   r   rA   rK   s    rR   )test_manualintegrate_trivial_substitutionr      s    CFS!W,a/3A2wAFFFAAaD1aR5L!+Q/	!QB%'1	1a 334 4 4rT   c                  6   [        SS[        S-  -
  -  [        5      [        [        S-
  5      * S-  [        [        S-   5      S-  -   :X  d   e[        SS[        S-  -   -  [        5      [        [        S-
  5      S-  [        [        S-   5      S-  -
  :X  d   eg )NrW   rY   rV   rZ   )rD   rO   r   r\   rT   rR   test_manualintegrate_rationalr      s    1a!Q$h<+AE
{1}s1q5z!|/KKKK1b1a4i=!,AE
1s1q5z!|0KKKKrT   c            
      
   S[        [        S-  * S-  5      -  S[        S5      -  [        [        5      -  [	        [        S5      [        -  S-  5      -  p[        X5        S[        S[        S-  -  5      -  S[        [        5      -  [        S[        -  5      -  S-  p[        X5        [        [        SS5      -  [        [        * S-  5      -  S[        [        SS5      [        S-  5      -  p[        X5        [        S[        -  5      [        -  [        S[        -  5      p[        X5        [        SS[        -  -   [        S-  -
  5      [        [        5      [        S5      -  [	        [        S-
  5      -  S-  p[        X5        [        [        S-  S[        -  -   S-   5      n [        S5      [        [        5      -  [        S5      * [        [        S5      S[        -  S-   -  S[        [        5      -  -  5      -  [        S5      [        [        S5      S[        -  S-   -  S[        [        5      -  -  5      -  -   -  S-  n[        X5        [        S[        S-  -  5      [        S5      [        [        5      -  [        S[        S5      -  [        -  [        [        5      -  5      -  S-  p[        X5        [        S[        -  S-   5      [        -  [        S5      [        S[        -  5      -  [        S5      [        S[        -  5      -  -   p[        X5        [!        S[        -  S-
  5      [        -  [!        S5      * [#        S[        -  5      -  [%        S5      ['        S[        -  5      -  -   p[        X5        S[        S[        -  S-
  5      -  [        -  S[        S5      -  [        S[        -  5      -  S[        S5      -  [        S[        -  5      -  -   p[        X5        [%        [        S-  5      [        -  [#        [        S-  5      p[        X5        [        [        S-  5      [        -  [        [        S-  5      S-  p[        X5        S[)        S[        -  S-   5      -  [+        S[        -  S-   5      S-  p[        X5        [-        SS[        -  5      [        -  [-        SS[        -  5      p[        X5        S[        SS[        [        5      S-  -  -
  5      -  S[        S5      -  [/        [        [        SS5      5      -  S-  p[        X5        [        SS[        [        5      S-  -  -   5      S[1        [        [        S	S5      5      -  p[        X5        g )
NrY   rV   r_   rW   rp   irf   r`   i)r   rO   r   r   r2   rS   r3   r
   r7   r/   r'   r4   r#   r5   r.   r1   r   r-   r   r0   r   r6   r@   r,   r+   rQ   s     rR   test_manualintegrate_specialr     s   S!Q$q\>1T!W9T"X-c$q'!)A+.>>q!S1a4[=!DH*T!A#Y.q0q!hq!nS!AY&Jx1~qs,K(Kq!qs8A:r!A#wq!q1Q3wA~RQAE
 :1 <q!AqD1Q3JNA	ab	CF78DGQqS1W,=qbz,J#KKAxQ1q)1T"X:6778 
99:
;A!qAv;QR(!DG)A+d2h2F)GGIq!qsQw<>3q6"QqS'>CF2ac7N:q!!a=?T!WHS1X-QAaC0@@q!S1q\>!Qs1vXb1g-#a&AaC0@@q!!9Q;AaCq!q!t9Q;1a4
q!S1q\>2acAg;q=q!1ac?1ga1oq!T!aA	k/""Ad1gIjHQN.K$KA$Mq!Ac!faiK !Jq(2q/$B"Bq!rT   c            	      >   [        [        [        [        S-  S[        -  -   S-   5      -  [        5      [        [        S-  S[        -  -   S-   -  :X  d   e[        [        [        S-  S[        -  -   S-   [        5      [        5      [        [        [        S-  S[        -  -   S-   [        5      5      :X  d   e[        [        [        [        5      [        [        [        [        5      [        5      [        [        [        5      [        [        [        5      :X  d   eg )NrV   r_   )rD   r   r   rO   ra   rA   r'   r\   rT   rR   test_manualintegrate_derivativer   )  s    2
1a4!A#:> ::A>
adQqSj1n  :adQqSj1na8!<AqD1Q3JNA./0 0 0:c!faAq91=3q61a#$ $ $rT   c            	         [        [        S[        -  S-   5      [        S[        -  S-   5      S-  5        [        [        S[        -  S5      [        S[        -  5      S-  5        [	        [        [
        [        [        -  -   S5      [        5      [        [        [
        [        [        -  -   5      [        -  [        [        S5      4[        [        [
        S5      -  S45      :X  d   e[        [        [        S-  S-
  S5      S[        [        S-  S-
  S5      -  5        [	        [        [        5      [        5      [        [        [        5      -  :X  d   e[	        [        [        S5      -  [        5      [        S-  S-  :X  d   e[	        [        [        S5      -  [        5      S:X  d   e[	        [        [        [        5      -  [        5      [        S-  [        [        5      -  S-  :X  d   e[	        [        [        [        * 5      -  [        5      [        S-  [        [        * 5      -  S-  :X  d   e[	        [        S[        -  S-   5      [        5      [        S-   [        S[        -  S-   5      -  :X  d   e[	        [        [        [        5      -  [        5      [        S-  [        [        5      -  S-  :X  d   e[	        [        [        S-   5      [        S[        -
  5      -  [        S-  -  [        5      [        S-  S-  [        SS5      -   [        [        S-   5      -  [        SS5      -
  [        [        * S-   5      -  :X  d   e[        S5      n [	        [        S	[        -   5      [        S[        -  S	-
  5      -  [        5      [        [        S	-   5      * [        [        S
S5      5      -   [        S[        -  [        S	5      -
  5      -  :X  d   e[	        [        U [        -   5      [        S[        -  U -
  5      -  [        5      [        U [        SS5      -  5      [        [        U -   5      -
  [        S[        -  U -
  5      -  :X  d   eg )Nr_   rV   r   rW   Tr{   rY   ra   rr      )rS   r*   rO   r)   rD   rv   ry   r   r   r
   r   r'   r#   r   )ra   s    rR   test_manualintegrate_Heavisider   2  sf   *QqSU+Yqs1u-=a-?@*QqS!,i!nQ.>?:a!eQ/3:a!A#g&q("Q(3a
1a8H6H$5OPQ Q Q*QqSUA.*QqSUA2F0FG9Q<+q1~===1Yq\>1-Aa7771Yr]?A.!3331Y]?A.!Q$y!}2DQ2FFFF1Yr]?A.!Q$y!}2DQ2FFFF9QqS1W-q1ac9QqS1W;M5MMMM1Yq\>1-Ail1B11DDDD9QU+Ia!e,<<QTA1E
Q$q&8Aq>
!9QU#3	3hq!n	DiQRPRUVPVFWWX X X 	sA3q1u:i!a&88!<1q5z\CQ00)AaC!A$J2GGH H H 3q1u:i!a&88!<8Aq>!"SQZ/1Q371CCD D DrT   c                  8   [        S5      n S[        SS5      p![        XU[        5      [	        X[        5      [        U [        5      [        U [        5      [        U [        5      [        U [        5      [        U [        5      [        X[        5      /nU GHn  n[        U[        5      nS HP  n UR                  X5      nUR                  X5      R                  [        5      U-
  R                  5       S:X  a  MP   e   [        UR                  [        S[        -  S-   5      -  n[        U[        5      nS	 HM  nUR                  X5      R                  [        5      UR                  X5      -
  R                  5       S:X  a  MM   e   [        S
5      n	[!        [#        UR$                  5      S-
  5       HJ  n
['        UR$                  5      nXU
'   [)        [        UR*                  " U6 U	5      [,        5      (       a  MJ   e   GMq     g ! [         a     GMl  f = f)Nnrr   rf   r_   )r{   rZ   r   rW   r_   rf   rp   r   rV   rW   )rV   rY   rr   t)r   r
   r=   rO   r;   r9   r:   r?   r<   r>   r8   rD   subs
ValueErrorr   r   rangelenargslist
isinstancefuncrA   )r   rv   ry   polyspintegraldegp_subbedqr   inew_argss               rR   $test_manualintegrate_orthogonal_polyr   J  s   Ahq!nqA!QA!!4jA6F1a(1a.'!Q-!QqQ!E "1a(*C66!> MM!)..q1H<DDF!KKK + affQ!a  "1a(CMM!)..q1AFF1NBJJLPQQQQ  CLs166{Q'AAFF|HQKoaffh.?CXNNNN (%   s   0H


HHc                  (   [        [        SR                  5       5      u  pn[        SSSS9n[        X1U-
  -  5      [        X1-  5      -  nU[        * [        4n[        XA5      X1-  S-  [        SU-  U-  5      S-  -   [        X2-  5      -  [        X2-  5      [        X1-  5      S-  -  S-  -
  U-  :X  d   eU [        XE5      R                  5       -  [        -  U [        X2-  5      -  :X  d   e[        XE5      R                  [        5      (       a   eg )Nzr x phir   T)integerpositiverV   rY   )mapr   splitr#   r   rD   r'   rB   trigsimphasr   )rrO   phir   	integrandlimitss         rR   test_issue_6799r   h  s   FIOO-.IA#sD40AQ#YAC(I"b\F9(
#a%#ac!e*Q,
AE
	*SZAC!-CA-E	EqHI I Iy+4466;q3qw<?OOOO+//66666rT   c                      [        [        [        -  [        5      [        [        [        S-   -  [        S-   -  [	        [        S5      4[        [        5      S45      :X  d   eg )NrW   rZ   T)rD   rO   ra   r   r   r   r\   rT   rR   test_issue_12251r   u  sO    1a4#y	
QUQU	R2Y'#a&$(9 9 9 9rT   c            	      Z   [        [        [        [        [        S-  -   5      5      [        5      [        [        [        S-  -   5      :X  d   e[	        [        [        [        S-  5      -  [        SS9[
        * [        [        5      -  [        [
        [        S-  -  5      -  S-  :X  d   eg )NrV   rY   F)risch)	rD   r   r   rO   rB   r	   r   r   r2   r\   rT   rR   test_issue_3796r   z  sw    4A1H.2c!ad(mCCCQQT]AU3r$r({3qAv;7Nq7PPPPrT   c                     [        [        [        5      [        [        5      -  [        SS9[        [        5      [        [        5      -  S-  [        [        5      [	        [        5      -  S-  -
  :X  d   e[        [        [        5      [	        [        5      -  [        SS9[        [        5      S-  S-  [	        [        5      S-  * S-  4;   d   eg )NTmanualrV   )rB   r   rO   r'   r#   r\   rT   rR   test_manual_truer     s    SVc!f_a5	Q#a&AQ#a&A 556 6 6SVc!f_a5	Q1q3q619*q.)* * *rT   c                  	   [        S5      n [        S5      n[        U [        -  [        5      [        U [        -  [	        U 5      -  [        [	        U 5      S5      4[        S45      :X  d   e[        X[        -  -  [        5      [        [        X[        -  -  [	        U 5      -  [        [	        U 5      S5      4U[        -  S45      U-  [        US5      4[        S45      :X  d   e[        [        U[        -  5      [        5      [        [        U[        -  5      U-  [        US5      4[        S45      :X  d   e[        SSS9n [        U S-   [        -  [        5      U S-   [        -  [	        U S-   5      -  :X  d   e[        SSS9n [        U S-   [        -  [        5      [        :X  d   e[        S5      n [        SSS9n[        X[        -  -  [        5      [        X[        -  -  [	        U 5      -  [        [	        U 5      S5      4U[        -  S45      U-  :X  d   e[        SSS9n [        U S-   U[        -  -  [        5      U S-   U[        -  -  U[	        U S-   5      -  -  :X  d   e[        S	SS
9n[        S5      n[        SX#[        S-  -  -   -  [        5      [        [        [        X#-  5      -  5      U[        X#-  5      -  -  :X  d   e[        SSS
9n[        SX#[        S-  -  -   -  [        5      [        [        [        U* 5      [        SU-  5      -  -  5      U[        U* 5      -  [        SU-  5      -  -  :X  d   e[        S[        U-  X-  -   S-   [        U[        S-  -  S-   5      -  -  [        5      X* -  [        [        U* -  X* -  [        U[        S-  -  S-   5      -  [        U* -  [        U[        S-  -  S-   5      -  -   S[        U* -  -  X* -  -  [        U[        S-  -  S-   5      -  -   -  [        5      -  :X  d   e[        S[        S-  S-   [        S[        S-  -  S-   5      -  -  [        5      [        S[        S-  S-   [        S[        S-  -  S-   5      -  -  [        5      :X  d   e[        S[        U[        -  -
  [        US-  -  -   -  [        5      [        SU[        -  * US-  [        -  -   [        -   -  [        5      :X  d   eg )Nra   r   r   Tr   rW   )zero)nonzerorv   negativery   rV   rZ   rY   )
r   rD   rO   r   r   r   r   r"   r   rA   )ra   r   rv   ry   s       rR   test_issue_6746r     s   sAsA1a4#y	
Ac!fbQm$q$i(1 1 1 11s8Q'9	1Xc!f_bQm,qS$K

 
 1X	 
D	,    3qs8Q'9	QqS!R1XD	,+ + + + 	sT"AAEA:q)a!eaZAE
-BBBBsAAEA:q)Q...sAsD!A1s8Q'9	
qS#a&"SVQ-(1Q3+,778,9 9 9 9sT"AAEQqS>1-	
Q!A##a!e*%& & &sT"AsA1aAqD&j>1-aQS	k1BAd13iK1PPPPsT"A1aAqD&j>1-QaRbd#$%qqbz$r!t*'<=> > >1q!tad{QQq!tVaZ0@@A1E	BaR!b'$qAvz*:":	QBQq!tVaZ  #!#$Q!W9QW#4T!AqD&1*5E#E#F GHIK 	KK K K 1q!taxa1fqj)99:A>QTAXtAadFQJ//0!45 5 51a!Q$h1a4/0!4QTEAqDFNQ&'+, , ,rT   c                     [        [        [        5      [        [        5      -  [        5      [        * [        [        5      -  [	        [        S-  * S-   5      -
  [        [        [        5      -  [	        [        S-  * S-   5      -   [        [        5      -  -   [        [	        [        S-  * S-   5      [        -  [        5      -
  :X  d   e[        [        [        5      [        [        5      -  [        5      [        * [        [        5      -  [	        [        S-  * S-   5      -   [        [        [        5      -  [	        [        S-  * S-   5      -
  [        [        5      -  -   [        [	        [        S-  * S-   5      [        -  [        5      -   :X  d   e[        [        [        5      [        [        5      -  [        5      [        * [        [        5      -  [        [        [        5      -  [        [        S-  S-   5      S-  -
  [        [        5      -  -   [        [        S-  S-   5      S-  -   [        [        [        S-  S-   5      [        -  [        5      S-  -   :X  d   eg )NrV   rW   )rD   r!   rO   r   r   rA   r   r"   r\   rT   rR   test_issue_2850r     s   473q6>1-!DGdAqD519o1May4A	?*CF2235=dAqD519oa>OQR5S2T T T T473q6>1-!DGdAqD519o1M	
47T1a4%!)_	$c!f,2-/7adUQY8I1/M2N N N N473q6>1-!DGqay1qM!O@ V?$ 2$&)!Q$(mAo268@QTAXqRS8TUV8V2W W W WrT   c            
         [        [        S[        -  5      [        [        5      -  [        5      [        [        5      [        S[        -  5      -  S-  S[        [        5      -  [	        S[        -  5      -  S-  -
  :X  d   e[        [        S[        -  5      [        [        5      -  [        5      R                  5       (       a   e[        [        S-
  [        S-  S[        -  -
  S-   S-  -  [        5      [        [        [        S-  S[        S-  -  -
  S[        S-  -  -   S[        -  -
  S-   -  [        5      S[        S[        S-  S[        S-  -  -
  S[        S-  -  -   S[        -  -
  S-   -  [        5      -  -
  :X  d   eg )NrV   rf   r_   rY   rp   rW   )rD   r'   rO   r   r#   rG   contains_dont_knowrA   r\   rT   rR   test_issue_9462r     sD   3qs8CF?A.#a&QqS/!2CaAhsSTUVSVxFWXYFY2YYYYc!A#hs1voq1DDFFFFAEadQqSj1nq%88!<#Aq!ta1f}qAv'=!'Ca'G$H!Lx1a4!AqD&=1QT6+AAaC+G!+K(LaPPQQ Q QrT   c                  L   [        [        5      [        [        S-  5      -  n S[        [        S-  5      -  [        [        5      -  S-  S[        [        S-  5      -  [        [        5      -  S-  -   n[	        U [        5      U:X  a  UR                  [        5      U :X  d   e[        [        [        5      -  [        [        S-  5      -  n [        S[        [        S-  5      -  [        [        5      -  S-  S[        [        S-  5      -  [        [        5      -  S-  -   -  S[        [        S-  5      -  [        [        5      -  S-  -
  S[        [        S-  5      -  [        [        5      -  S-  -   n[	        U [        5      U:X  a  UR                  [        5      U :X  d   eg )NrY   ru         !     )r#   rO   r   r'   rD   r   rQ   s     rR   test_cyclic_partsr     s>   As1Q3xA
3qs8CF2#ac(
3q6 1" 44A1a A%!&&)q.88	#a&QqSA	
Bs1Q3xKAr!Ac!A#hJs1v$5b$88	9C!HSVC
 "%c!A#h,s1v"5c"9
:A1a A%!&&)q.88.rT   c                     [        S[        S-  -  S[        S-  -  -   S[        S-  -  -   S[        -  -   S-   [        S-  S[        S-  -  -   S[        S-  -  -   S[        S-  -  -   S[        S-  -  -   S[        -  -   S	-   -  [        5      S[        -  [        S-  S	-   -  S[        [        5      -  -   S	[        S-  S	-   -  -
  S[        S	-   -  -
  :X  d   eg )
NrY   r_   ru   rV      rp   rX   rf   rW   )rD   rO   r"   r\   rT   rR   test_issue_10847_slowr     s    AadFQq!tVObAg51<q@dQq!tVma1f4qAv=!Q$F1LqPRSTVQ31q>Ad1gI51a4!8Dq!a%yPQ Q QrT   c                  2   [        [        S-  [        S-  [        -
  -  [        5      [        [        [	        [        [        [        * 5      -  5      [        [        * 5      -  [        [        S5      4S[        -  S45      -  [        -   :X  d   e[        SSS9n [        [        S-  [        S-  U -
  -  [        5      U [        [	        [        [        U * 5      -  5      [        U * 5      -  U S:  4[        [        U 5      * [        -   5      [        [        U 5      [        -   5      -
  S[        U 5      -  -  S45      -  [        -   :X  d   e[        [        [        [        -
  5      [        [        [        -  5      -  [        5      S[        S-  -  [        [	        [        [        [        -
  5      [        [        5      -  5      [        [        5      -  [        [        S5      4S[        [        [        -
  5      -  S45      -  S-  S[        -  [        [        [        -
  5      -  S-  -
  S[        [        -
  [        SS5      -  -  [        [        [        -  5      -  S-  -   S[        [        -
  [        SS5      -  -  S	-  -   :X  d   e[        S
SS9n[        SSS9n[        [        [        U-
  5      [        U[        -  5      -  [        5      SUS-  -  [        [	        [        [        U-
  5      [        U5      -  5      [        U5      -  US:  4[        [        U* 5      * [        [        U-
  5      -   5      [        [        U* 5      [        [        U-
  5      -   5      -
  S[        U* 5      -  -  S45      -  S-  SU-  [        [        U-
  5      -  S-  -
  S[        U-
  [        SS5      -  -  [        U[        -  5      -  S-  -   S[        U-
  [        SS5      -  -  S	-  -   :X  d   e[        [        [        5      [        [        5      -  [        5      S[        [        SS5      -  -  [        [        5      -  S-  S[        [        SS5      -  -  S	-  -
  :X  d   e[        [        [        [        -  [        -   5      [        -  [        5      nU[        S[        -  [        [	        [        [        [        -  [        -   5      [        [        * 5      -  5      * [        [        * 5      -  [        [        S5      4S[        [        [        -  [        -   5      -  S45      -  S[        [        [        -  [        -   5      -  -   [        [        S5      4[        [        5      [        [        5      -  S45      :X  d   e[        U5      [        S[        -  [	        [        [        [        -  [        -   5      [        [        * 5      -  5      -  [        [        * 5      -  S[        [        [        -  [        -   5      -  -   [        [        S5      [        [        S5      -  4S[        -  [        [        [        -  [        -   5      -  S[        [        [        -  [        -   5      -  -   [        [        S5      4[        [        5      [        [        5      -  S45      :X  d   e[        SSS9n[        SSS9n[        [        U[        -  U-   5      [        -  [        5      [        SU-  [        [	        [        U[        -  U-   5      [        U* 5      -  5      * [        U* 5      -  US:  4[        * [        [        U5      * [        U[        -  U-   5      -   5      [        [        U5      [        U[        -  U-   5      -   5      -
  -  S[        U* 5      -  -  S45      -  S[        U[        -  U-   5      -  -   [        US5      4[        U5      [        [        5      -  S45      :X  d   e[!        [        [        U[        -  U-   5      [        U -   -  [        5      5      [        SU-  U -  [        [	        [        U[        -  U-   5      [        X@-  U-
  5      -  5      [        X@-  U-
  5      -  X@-  U-
  S:  4[        [        U* U -  U-   5      * [        U[        -  U-   5      -   5      S[        U* U -  U-   5      -  -  [        [        U* U -  U-   5      [        U[        -  U-   5      -   5      S[        U* U -  U-   5      -  -  -
  S45      -  SU-  [        [	        [        U[        -  U-   5      [        X@-  U-
  5      -  5      [        X@-  U-
  5      -  X@-  U-
  S:  4[        [        U* U -  U-   5      * [        U[        -  U-   5      -   5      S[        U* U -  U-   5      -  -  [        [        U* U -  U-   5      [        U[        -  U-   5      -   5      S[        U* U -  U-   5      -  -  -
  S45      -  -   S[        U[        -  U-   5      -  -   [        US5      4[        U5      [        U [        -   5      -  S45      :X  d   e[        [        S[        -  S-   5      [        S-   -  [        5      S[        S[        -  S-   5      -  [        [        S[        -  S-   5      S-   5      -
  [        [        S[        -  S-   5      S-
  5      -   :X  d   e[        [        S[        -  S-   5      S-  [        -  [        5      S[        -  S-   [        SS5      -  S-  S[        -  S-   [        SS5      -  S-  -
  :X  d   e[        [        [        SS5      -  [        [        5      -  [        5      S[        [        SS5      -  -  [        [        5      -  S-  S[        [        SS5      -  -  S-  -
  :X  d   e[        [        S-  [        [        5      -  [        5      [        [        5      * S[        S-  -  -  SS[        S-  -  -  -
  :X  d   e[        [        [        5      [        S-  SS[        -  -
  -  -  [        5      [        [        5      [        SS[        -  -   5      -  [#        [        SS[        -  -   5      [        -  [        5      -
  :X  d   eg )NrV   r   rZ   Tcrw   rY   r_   r`   ra   zr{   rW   rv   ry   rf      r   rk   )rD   rO   r   r   r"   r   r   r   r   ra   r   r
   rv   ry   r   r	   r   rA   )rcryrzrh   r|   r}   s         rR   test_issue_10847r     s`    1a41a4!8,a0	)T!D!H*%dA2h.1a9BqD$<
HH1LM M M 
$	B1a41a4"9-q1
9d1T2#Y;'bS	126:DH9q=)CR1,==$r(
KTRT 	TVW	XX X X 4A;QU3Q7	!Q$y$tAE{4723DG;R1XFT!a%[.$/1 	112	356qSa!e_Q5F	G	1q58Aq>
!!#ac(*1,	-/0!a%(1a.1H/H/J	KK K K 
$	B	$	B4B<#b1f+5q9	"a%	4QVT"X 56tBx?aHbS	zDRL89CbS	DQRUWQWL@X<YY\]^bdfcf^g\ghjnoq 	qqr	sR4QV,Q.	/12AFXa^3K1KCPRSTPTI1UVW1W	X a"fx1~55a7	88 8 8 47SV+Q/1QA5F3Fs1v3Ma3ORSTUW_`acdWeTeRefgRg3ggggT!A#']Q.2FY1Y
tAaC!G}T1"X%
&	&tQBx	/Aq:	
4!a=$&! !!#$T!A#']?!346q!H > 
aQ        &!Y	
1T$qsQw-aR()	)$r(	2QtAaC!G}_	DbAhQSTUWXQYFYZ	Ad1Q37m	aQqS1Wo	-r!Qx8	aQ&       
 
$	B	$	B41r	?Q.2U9tBqD2ItRCy011$s);R!VDS$r(T"Q$)_45DHtBqDSUI<V8WWXZ[\`bdad\eZefhlmo o tBqD2I !#2q	+ "Xc!f_d#	%% % % /$r!tby/QV"<a@AbeBhy$tBqD2ItBEBJ?O/O*PQUVXV[^`V`Qa*acechkmcmpqcq)r(+T2#b&2+->,>bdRi,P(QSTUY[]Z]^`Z`ceZeUfSf(g(+D"R",=RTBY,O(PRSTXZ\Y\]_Y_bdYdTeRe(f)ghl(n o o d9d41r	?4
;K+K&LTRTRWZ\R\M]&]_a_dgi_ilm_m%n%($s2v{*;);d2a4"9o)M%NPQRVXZWZ[]W]`bWbRcPc%d%(rc"frk):T"Q$)_)L%MqQUWYVYZ\V\_aVaQbOb%c&dei%kl ll RTBY'( *,B4 7;2hs26{6JD5QSS S S 4!a=AE2A6!D1qM/CPTUVWXUX[\U\P]`aPaLb:behimnopqnqtunuivyzize{:{{{{4!a=1,q0!41q8Aq>8QRT8TXYZ[X[^_X_bjklnobpWpqrWr8rrrr1hqm+c!f4a8Aa!A>N<NsSTv<UVW<WZ[\]_ghijk_l\lZlmoZo<oooo1r7SV+Q/CF7AadF3Ca1a4j3PPPP3q61a4QqS>2A6As2!8}xB1Ha;;< < <rT   c            	         [        [        [        [        5      R	                  [        5      [        5      [        [        [        [        [        5      [        5      [        5      :X  d   e[        [        [        [        5      R	                  [        5      R	                  [        5      [        5      [        [        [        [        5      [        5      :X  d   eg rN   )rD   rK   rO   ra   r   rA   r   r\   rT   rR   test_issue_12899r     st    1Qq6;;q>!,AaF19Ma0PPPP1Qq6;;q>..q1!4
1Qq6!8LLLLrT   c                      [        [        [        [        SS45      [        5      [        [        [        [        SS45      -  :X  d   eg )NrW   rV   )rD   rA   ra   rO   r\   rT   rR   #test_constant_independent_of_symbolr     s=    8A1ay115	(1q!Qi
  ! ! !rT   c                  &   [        [        S[        -  5      [        5      [        S[        -  5      * S-  :X  d   e[        [        [        5      [        S[        -  5      -  [        5      S[        [        5      S-  -  S-  :X  d   e[        [        S[        -  5      [        [        5      -  S[        [        5      -   -  [        5      S[	        [        [        5      S-   5      -  [        [        5      S-  -
  S[        [        5      -  -   :X  d   eg )NrV   r{   r_   rW   )rD   r'   rO   r#   r   r\   rT   rR   test_issue_12641r     s    3qs8Q'C!H9Q;6663q6#ac(?A."SVQY,q.@@@C!HSVOa#a&j91=
3s1vz?SVQY&3q612 2 2rT   c                      [        [        [        5      [        [        5      S-  -  [        5      [        [        5      S-  * S-  :X  d   eg )Nrf   rX   )rD   r'   rO   r#   r\   rT   rR   test_issue_13297r      s6    3q6CFAI-q1c!faiZ!^CCCrT   c            
          [        S[        [        [        S-   5      -  -  [        [        [        S-   5      S-
  5      [        [        [        S-   5      S-   5      -
  5        g )NrW   )rS   rO   r   r   r\   rT   rR   test_issue_14470r   %  sF    !QtAE{]+Sa!eq-ACQQRUVWDX-XYrT   c            	         [        [        [        5      [        [        [        5      5      -  [        5      [	        [        [        5      5      :X  d   e[        [        S[        -  5      [        [        [        5      5      -  [        5      [        [        5      [	        [        [        5      5      -  [        [        [        5      5      -   :X  d   e[        [        S[        -  5      [	        [        [        5      5      -  [        5      n U R                  [        5      (       a   eU R                  [        5      [        S[        -  5      [	        [        [        5      5      -  :X  d   e[        [        S [        SS5       5       5      [        5      [        [        S[        -  5      -  S-  [        [        S[        -  5      -  S-  -   [        [        S[        -  5      -  S-  -   [        [        S	[        -  5      -  S	-  -   [        [        S
[        -  5      -  S
-  -   [        [        S[        -  5      -  S-  -   [        [        [        5      -  -   [        S[        -  5      S-  -
  [        S[        -  5      S-  -
  [        S[        -  5      S-  -
  [        S	[        -  5      S-  -
  [        S
[        -  5      S-  -
  [        S[        -  5      S	-  -
  [        [        5      -
  :X  d   eg )NrV   
   c              3   T   #    U  H  n[         [        U[         -  5      -  v   M      g 7frN   )rO   r   ).0ks     rR   	<genexpr>"test_issue_9858.<locals>.<genexpr>2  s     ?;aqQqSz;s   &(rW   rp   rr   rX   rf   rY   r_   r   $   r   ru   r`   )
rD   r   rO   r#   r'   r   rA   r   sumr   )ress    rR   test_issue_9858r   )  s%   3q6#c!f+-q1SQ[@@@3qs8CAK/3As3q6{SQ[() ) )
#bd)CAK/
3Cwwx    88A;#bd)CAK////3?5A;??C	#ac(
1qQqSz!|#aAaCjl2Qs1Q3xZ\A	#ac(
1	QqSz!|	$&'Ah	/14QqS"	=>A!A#hrk	JAaC	!A#hrk	"$'!HQJ	/14QqS!	<>A!f	EF F FrT   c                     [        [        [        S-  S-   -  [        5      [        [        S-  5      S-  :X  d   e[        [        S-  [        S-  S-   -  [        5      [        [        S-  S-  5      S-  :X  d   e[        S	[        S-  -  S-   S-  -  n [        U [        5      R                  [        5      R	                  5       U :X  d   eg )
NrY   rW   rV   rX   r   r_   rf   r   r`   )rD   rO   r"   r   factorr   s    rR   test_issue_8520r   8  s    1adQh<+tAqDz!|;;;1a4A+Q/41Q<?BBB	1QT6A:/A1a %%a(//1Q666rT   c                  \  ^ ^^ [        S5      u  mm[        T5      [        T5      -   m [        T [        T5      T5      T[        [        T5      5      -   :X  d   e[        T [        T5      T5      [        T5      T-   :X  d   e[	        [
        U U4S j5        [	        [
        U UU4S j5        g )Nzx yc                     > [        T T5      $ rN   )rH   )exprrO   s   rR   <lambda>"test_manual_subs.<locals>.<lambda>G  s    {43rT   c                  2   > [        T [        T5      TT5      $ rN   )rH   r   r   rO   ra   s   rR   r   r   H  s    {4QA>rT   )r   r   r   rH   rI   r   r   s   @@@rR   test_manual_subsr   ?  s    5>DAqq6CF?DtSVQ'1s3q6{?:::tSVQ'3q6A:555
:34
:>?rT   c                  H   [        [        5      [        [        [        5      5      -  [        [        SS5      -  -  n S[        [        SS5      -  -  [	        [        [        5      5      -  S-  S[        [        SS5      -  -  [        [        [        5      5      -  S-  -   S[        [        SS5      -  -  [	        [        [        5      5      -  S-  S[        [        SS5      -  -  [        [        [        5      5      -  S-  -   [        [        5      -  -   n[        X5        g )	Nr_   rY   irW   r   r   ru   r   )r   rO   r#   r
   r'   rS   rQ   s     rR   test_issue_15471r   K  sH   As3q6{1hq!n,,AQAs3q6{*3.QA5F1Fs3q6{1RSV1VVZ\]^`hijlm`n]nZnorsvwxsyozZz{}Z}  AB  CD  FN  OP  RS  FT  CT  AT  UX  Y\  ]^  Y_  U`  A`  ac  Ac  [c  eh  ij  ek  Zk  	kA!rT   c                     S[         -  S-   S[         S-  -  S[         -  -
  S-   -  n [        U [         5      S[        S[         S-  -  S[         -  -
  S-   5      -  S-  S[        S5      -  [	        S[        S5      -  [         [        SS5      -
  -  S-  5      -  S	-  -   :X  d   eSS[         S-  -  S[         -  -   S-   -  n[        U[         5      S[        S
[         -  S-   5      -  S[        S
[         -  S
-   5      -  -
  :X  d   eg )Nrf   rV   r_   rp   rX   rg      rW   E   rY   )rO   rD   r   r   r"   r
   )rK   gs     rR   test_quadratic_denomr   R  s    	
1q1QT6AaC<!#$A1a Ac!AqD&1Q3,*:&;$;A$=48DQRSWXZS[Q[]^aijkmnao]oQpqsQsLt@tuw@w$wwww	1QT6AaC<!A1a Ac!A#'lNQs1Q37|^$CCCCrT   c                  r    [        [        [        5      [        5      [        [        [        5      -  :X  d   eg rN   )rD   r'   rO   ra   r\   rT   rR   test_issue_22757r  X  s#    3q61%SV333rT   c                      [        [        [        5      [        5      n U R                  R                  nUR                  UR
                  UR                  -  :X  d   eg rN   )rG   r(   rO   substepr   constantother)stepsconstant_times_steps     rR   test_issue_23348r  \  sI    3q61%E--//((,?,H,HK^KdKd,ddddrT   c                     [        S[        [        S-  S-
  5      -  [        SS45      R                  SS9n U [	        SS[        S5      -  -
  5      * [	        S5      -   :X  d   e[        U R                  5       5      S	:X  d   eg )
NrW   rV   r{   rZ   Tr   rY   r_   z1.31695789692482)rA   r   rO   doitr   strr   )r   s    rR   test_issue_23566r  b  sw    41q>!Ar2;/44D4AAQ47]##c!f,,,,qssu:++++rT   c            
         [        SSS9n [        SSS9n[        [        [        [        S-  -  [
        -   5      [        5      [        [        5      [        [
        5      -  [        [        [        5      [        -  5      -  S[        [        5      -  -  :X  d   e[        [        U [        S-  -  [
        -   5      [        5      [        [        5      [        [
        5      -  [        [        U 5      [        -  5      -  S[        U 5      -  -  :X  d   e[        [        U[        S-  -  [
        -   5      [        5      [        [        5      * [        [
        5      -  [        U[        -  [        U* 5      -  5      -  S[        U* 5      -  -  :X  d   e[        [        [        [        S-  -  [
        -   5      [        5      [        S5      [        [        5      -  [        [
        5      [        [        S5      [        [        5      -  [        -  [        [        5      -  5      -  [        [
        5      [        [        S5      [        [        5      -  [        -  [        [        5      -  5      -  -   -  S[        [        5      -  -  :X  d   e[        [        [        [        S-  -  [
        -   5      [        5      [        S5      [        [        5      -  [        [
        5      * [        [        S5      [        [        5      -  [        -  [        [        5      -  5      -  [        [
        5      [        [        S5      [        [        5      -  [        -  [        [        5      -  5      -  -   -  S[        [        5      -  -  :X  d   eg )NapTr   anr   rV   )r   rD   r   rv   rO   ry   r   r   r3   r2   r'   r4   r#   r5   )r  r  s     rR   test_issue_25093r  h  s   	t	$B	t	$B3qAvz?A.$r(3q6/$tAwqy/2QSTUYZ[U\S\2]]]]3r!Q$w{+Q/48CF?4RQR
CS3SUVW[\^W_U_3````3r!Q$w{+Q/DH9SV3CC1TSURUYDW3WYZ[_ac`c[dYd3eeee3qAvz?A.QR#a&$q'$q'/!*;DH*D!EE
a&$q'$q'/!+DH45
56 	789$q'		CD D D 3qAvz?A.QR3q6'(4747?1+<T"X+E"FF
a&$q'$q'/!+DH45
56 	789$q'		CD D DrT   c            
         [        [        [        S-  5      [        [        [        S-  5      -  S-  5        [        [        [        [        S5      S-  -  5      S[        -  [        [        [        S5      S-  -  5      -  S-  5        [        S[        [        S-  5      -  [        [	        [        5      -  [        [        S-  5      -  5        [        [        [        [        S-  5      -  [        S-  [        [        S-  5      -  [	        [        5      -  5        [
        [        [        [        -  -   [        -  -  [        -  n [
        [        [        [        -  -   [        -  -  [        -  [        [        -  [        -   -  [        [        -  S-   -  n[
        [        [        [        -  -   [        -  -  [        -  [        [        -  [        -   -  [	        [        [        -  [        -   5      -  n[        U [        5      [        [        U[        [        [        -  S5      4US	45      [        [        S
5      4[        [        [        -  [
        -  [        -  -  S	45      :X  d   eUR                  [        5      R                  U 5      (       d   eUR                  [        5      R                  [        [        -  S5      R                  U 5      (       d   eg )NrV   rf   r_   rX   rg   rW   rZ   Tr   )rS   r   rO   r   r   r   rv   ry   derD   r   r   r   rP   r   )rK   F1F2s      rR   test_nested_powr  v  s   $q!t*aQT
l1n5$q1Q46{+QqSa!A$q&k1B-B2-EF!DAJ,#a&ad(;<!DRM/1a4QU+;CF+BC	
AacEA:A
Q1WqL.1	acAg	&!a	0B
Q1WqL.1	acAg	&s1Q37|	3B1a 9b"QqS"+.T
;R1XFAqDQRFUV;X\H]^_ _ _771:Q771:??1Q3#**1----rT   c                  V	   [        S[        S-  -  S-   [        SS[        -  -   5      -  SS[        -  S-   [        S5      S-  -  -  S-  SS[        -  S-   [        S5      S-  -  -  S-  -
  S	S[        -  S-   [        S5      S-  -  -  S
-  -   S[        S[        -  S-   5      -  S
-  -   5        [	        [        [        [
        [        [        -  -   5      S-  -  [        5      [        [        S[        S-  [
        [        [
        [        [        -  -   5      -  [        [
        [        [        -  -   5      -   5      [        [        S5      4[        S-  S[
        [        S5      S-  -  -  -  S45      :X  d   e[        [        S[        -  S-   5      S-   S[        -  S-   S[        S5      -  -  S-   -  S[        S5      -  S[        -  S-   [        S5      S-  -  -  S-  S[        S5      -  S[        -  S-   [        S5      S-  -  -  S-  -
  S[        S5      -  S[        -  S-   [        R                  S-  -  -  S-  -
  SS[        -  S-   [        S5      S-  -  -  S-  -   SS[        -  S-   [        R                  S-  -  -  S-  -
  [        S5      [        S[        -  S-   5      -  S-  -   S[        S[        -  S-   [        R                  S-  -  S-   5      -  S-  -   S[        S5      -  [        S[        -  S-   [        R                  S-  -  5      -  S-  -   5        [        [        [        [        [        5      -   5      S[        [        [        5      [        -   5      -  [        [        5      S-  [        S-  -   [        S5      S-  -
  -  [        S[        [        5      -  S[        [        [        5      [        -   5      -  -   S-   5      S-  -   5        [        [        S[        -  S-   [        S[        -  S-   5      -   5      S-  [        S[        -  [        S[        -  S-   5      -   S-   5      S[        -  S-  SS[        -  S-   [        S5      S-  -  -  S	-  -   [        S[        -  S-   5      S	-  -   S[        -  S-   S-  S-  -   [        S5      S-  -   -  S-  5        g )Nrf   r_   rY   rV   r   rr   i7     (   Q      r{   r   TrW   rX      r   rp   r`   rg   )rS   rO   r   r   rD   rv   ry   r   r   r   Oner   r"   r\   rT   rR    test_manualintegrate_sqrt_linearr    sj   1QT6!8T!AaC%[0acAg1a004q!A#'QqT!V9L7LR7OOacAg1a003469$qsQw-6G6JKL 1T!AaC%[!^+Q/3q!R%4AaC=4AaC=!@A2a8LqRStUVWX[\]^[_`a[aWbUbOceiNjkl l l4!A;q=AaCEQqtV+<Q+>?DG)QqS1W!Q$77:QtAwY!aSTUVSWXYSYGZ=Z[]=]]DG)QqS1Wa$88:;=>!a1Q4PQ6?R=RST=TUWXZ[\]Z]`aZaefejejklelYmWmnoWopq'$qsQw-/1245c1Q37aeeAg:NQR:R6S4STU4UV DG)D!A#'QUU1W)=$>>q@AB
 $qay/Da1--tAwrzAaC/?!A$q&/HICPQRVWXRYPY\]^bcghicjmncn^o\oPorsPsLtuvLvvx$qs1uT!A#a%[0114qsT!A#']2Q67Q3r6B!a1Q46':$:2$==QqS1Wb@PPTUVWTWZ[T[^_S_`bSbbefgiejkmemmoopqrrT   c                     [        S[        [        [        -
  S-  S-
  5      -  [	        S[        -  S[        [        S-  S[        -  [        -  -
  S-
  5      -  -   S[        -  -
  5      5        [        S[        S[        S-  -  S[        -  -   S-   5      -  [        S5      [        S[        S5      -  [        [        S5      S-  -   -  S-  5      -  S-  5        [        S[        S[        S-  -  S[        -  -   S-   5      -  [        S5      [        S[        S5      -  [        [        S5      S-  -
  -  S-  5      -  S-  5        [        S[        S[        S-  -  S[        -  -   S-
  5      -  [        S5      [	        S	[        -  S[        S5      -  [        S[        S-  -  S[        -  -   S-
  5      -  -   S-   5      -  S-  5        [        S[        S[        S-  -  S[        -  -
  S-   5      -  [        [        R                  -
  [	        [        [        R                  -
  5      -  S[        [        [        R                  -
  S-  5      -  -  5        [        S[        [        [        [        -  -   [        [        S-  -  -   5      -  [        5      [        [	        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        S
5      [        [        [        S-  S[        -  -  -
  S
5      -  4[        S[        -  -  [        -   [	        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  [        [        S
5      4S[        [        [        [        -  -   5      -  [        -  [        [        S
5      4[        [        [        5      -  S45      :X  d   e[        S[        -  S	-   [        S[        S-  -  S[        -  -   S-   5      -  S[        S[        S-  -  S[        -  -   S-   5      -  S-  S[        S5      -  [        S[        S5      -  [        [        S5      S-  -   -  S-  5      -  S-  -   5        [        S[        -  S	-   [        S[        S-  -  S[        -  -   S-   5      -  S[        S[        S-  -  S[        -  -   S-   5      -  S-  S[        S5      -  [        S[        S5      -  [        [        S5      S-  -
  -  S-  5      -  S-  -   5        [        S[        -  S	-   [        S[        S-  -  S[        -  -   S-
  5      -  S[        S[        S-  -  S[        -  -   S-
  5      -  S-  S[        S5      -  [	        S	[        -  S[        S5      -  [        S[        S-  -  S[        -  -   S-
  5      -  -   S-   5      -  S-  -   5        [        [        [         [        -  -   [        [        [        [        -  -   [        [        S-  -  -   5      -  [        5      [        [        * [         -  S[        -  -  [        -   [        [	        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        [        S-  S[        -  -  -
  S
5      4[        S[        -  -  [        -   [	        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  S45      -  [         [        [        [        [        -  -   [        [        S-  -  -   5      -  [        -  -   [        [        S
5      4S[        -  [        [        [        [        -  -   5      -  S[         -  [        * [        [        [        [        -  -   5      -  [        [        [        -  -   [        S5      S-  -  S-  -   -  [        -  -   [        -  [        [        S
5      4[        [        -  [         [        S-  -  S-  -   [        [        5      -  S45      :X  d   e[        S[        S-  -  [        S-  -
  S[        -  -   S-
  [        [        S-  S[        -  -
  S-   5      -  [        5      [        [        S-  S[        -  -
  S-   5      [        S-  S[        -  S-  -   [        S5      S-  -   -  S[	        S[        -  S[        [        S-  S[        -  -
  S-   5      -  -   S-
  5      -  S-  -   :X  d   e[        [        S[        S-  -  S[        -  -
  S-   5      [        S-  [        S5      S-  -
  [        S[        S-  -  S[        -  -
  S-   5      -  S[        S5      -  [        S[        -  S-  [        S5      S-  -
  5      -  S-  -   5        [        [        [        [        [        S-  -  -   5      [        5      [        [        [        [	        S[        [        5      -  [        [        [        [        S-  -  -   5      -  S[        -  [        -  -   5      [        [        5      -  [        [        S
5      4[        [	        [        5      -  [        [        [        S-  -  5      -  S45      -  S-  [        [        [        [        [        S-  -  -   5      -  S-  -   [        [        S
5      4[        [        5      [        -  S45      :X  d   e[        [        [        [        [        -  -   [        [        S-  -  -   5      [        5      [        [        S-  [        S-  S[        -  -  -
  [        [	        [        S[        [        5      -  [        [        [        [        -  -   [        [        S-  -  -   5      -  -   S[        -  [        -  -   5      [        [        5      -  [        [        [        S-  S[        -  -  -
  S
5      4[        S[        -  -  [        -   [	        [        S[        -  -  [        -   5      -  [        [        [        S[        -  -  [        -   S-  -  5      -  S45      -  [        S[        -  -  [        S-  -   [        [        [        [        -  -   [        [        S-  -  -   5      -  -   [        [        S
5      4S[        [        [        -  -   [        S5      S-  -  -  S[        -  -  [        [        S
5      4[        [        5      [        -  S45      :X  d   e[        [        [        [        S-  S[        -  -   S-   5      -  [        S-  S-  [        S	-  -   [        S5      S	-  -   [        [        S-  S[        -  -   S-   5      -  S[        [        S5      [        S-   -  S-  5      -  S-  -
  5        g )NrW   rV   r_   rY   rf   rg   rk      rX   r   Trr   r`   irq      e   rp      ru   i  i iY  i+A  iiQ  iC)  ir+  i  i:C)rS   r   rO   r	   r   r   r   r!   r   rD   rv   ry   r   r   r   r  r  r\   rT   rR   #test_manualintegrate_sqrt_quadraticr%    s   !D!a%!A..AaC!DA!APQAQ<R:R4RUVWXUX4X0YZ!D1a4!A..QaRj!aPQdSTf*>UVX>X8Y0YZ[0[\!DAqD1Q//aaRj!aPQdSTf*>UVX>X9Y1YZ[1[\!D1a4!A..QAaC!DG)DQRSTVWSWQWZ[\]Z]Q]`aQaLbBb<bef<f8g0ghi0ij!D1a4!A..QVVSQVV_0LaPTVWZ[Z`Z`V`cdUdPeNe0fg1T!AaC%!Q$,//33q1T!W9T!ac'AadF*:%;;;ac!eCDT!WLbQRTUhY[\]`acd`dfghifi`j\jlmYnNnoqsGaKQ!Wq[!11$q!QqS'A+9I7I2JJBqRSHUT!ac']?1$bAh/!DG)T1B	DD D D
 1Q3q5$qAvacz!|"44D1a4!A#!12214qayqbzSTWXYZW[\]W]S]G^_aGaAb7bcd7ddf1Q3q5$r!Q$wqs{1}"55T"QT'AaC-!"344Q6DGD4PR8UVYZ[\Y]^_Y_U_I`acIcDd9def9ffh1Q3q5$qAvacz!|"44D1a4!A#!12214qayQqS1TRSW9UYZ[\]_`\`Z`cdefcfZfijZjUkKkEknoEoAp7pqr7rrtAacE4!A#a1f#55q9QBqD!A#JNc!aQiQ1WqAv5E0F&F"F1Q"NOPTUVPWWY[\]`acd`dfghifi`j\jlmYno !A#w{C1Q3!,<<T!Q!Wq[STDTBT=UUW[\^^ T!ac'AadF*++A-. 02!Qx9 aCQ1W%!aRQ1W-=QqSAaDQRF@STU@U-U(VWX(XXZ[[]_`acd]efaC!AqD&(NDG+T2	44 4 4 AadF1a4K!OA-tAqD1HQJ/??CQTAaCZ!^adRT!VmafQh67#c!A#$qRStVWXYVYz\]~J^H^B^abBb>c:cdf:ffg g g $uQTz%'1%78Q35%/eAqDj576JU6R1SS#DJ.uU1WU]QuXd]5R/SST^^_` 4!AqD&>1-1YAd1gId1qAv:.>$>1Q$F GQ OQSTUWXQYZ !#a&a1f 5t<> >>?@BCDQqRStVDTBTUVBVWXZ[\^_X`b719d#	%% % % 4!A#a1f-q1AaC!Q$!*$c!aQiQ1WqAv5E0F&F"F1Q"NOPTUVPWWY[\]`acd`dfghifi`j\jlmYno !A#w{C1Q3!,<<T!Q!Wq[STDTBT=UUW[\^^ qsGacM4AaC!AqD&(8#99: <>a8E a!A#g1a((!A#.1a9719d#	%% % % !DAac!,,a46AaC<!A$q&0$q!taczA~2FF5QUVWQXZ[^_Z_Q`abQbKcIcdeIeegrT   c            
         [        [        [        [        5      -  [        [        5      -  [        [        [        5      -  [	        [        [        5      [        [        5      -   5      -
  5        [        [        [        [        5      S-  -  [        [        [        5      -  [	        [        [        5      5      -   5        [        [        S-  [        [        [        5      [        S45      -  [        S-  [        [        [        5      [        S45      -  S[        S-  -  [        [        [        5      [        S45      -  -
  S[        -  [        [        [        5      [        5      -  -   S[        [        5      -  -
  5        g )NrV   r_   rY   rX   )rS   rO   r&   r(   r   r#   r   rK   r\   rT   rR   test_mul_pow_derivativer'    s    !CF(3q6/1SV8c#a&3q6/6J+JK!CFAI+qQx#c!f+'=>!Q$z!A$A77Q$z!A$A77!AqD&AaDSTVWRXAY:YYA#j1q11245adF;<rT   N)sympy.core.exprr   sympy.core.mulr   sympy.core.functionr   r   r   r   sympy.core.numbersr	   r
   r   sympy.core.relationalr   sympy.core.singletonr   sympy.core.symbolr   r   r   &sympy.functions.elementary.exponentialr   r   %sympy.functions.elementary.hyperbolicr   r   r   r   r   r   r   (sympy.functions.elementary.miscellaneousr   $sympy.functions.elementary.piecewiser   r   (sympy.functions.elementary.trigonometricr   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   'sympy.functions.special.delta_functionsr)   r*   *sympy.functions.special.elliptic_integralsr+   r,   'sympy.functions.special.error_functionsr-   r.   r/   r0   r1   r2   r3   r4   r5   r6   'sympy.functions.special.gamma_functionsr7   #sympy.functions.special.polynomialsr8   r9   r:   r;   r<   r=   r>   r?   &sympy.functions.special.zeta_functionsr@   sympy.integrals.integralsrA   rB   sympy.logic.boolalgrC   sympy.integrals.manualintegraterD   rE   rF   rG   rH   sympy.testing.pytestrI   rJ   rO   ra   r   r[   r   rv   ry   r   r  r  rK   rS   r]   rb   rd   ri   rn   rs   r~   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r  r  r  r  r  r  r%  r'  r\   rT   rR   <module>r>     s/      D D 0 0 $ " 6 6 = ] ] ] 9 J w w w w I O m m m > J  J  J : ; #. . -&'<= 1aAq!Q1SMT d 
@
@
13&8> 3 3" _& _&D
F4L
" J$D0O< 	7 	79
Q
*%,P W WQ9 Q Q :< :<zM
!
2 D DZ F F7	@    D4e,D.r$,g^<rT   