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DerivativeÚdiffÚIÚsqrtÚerfÚ	PiecewiseÚNeÚsymbolsÚRationalÚAndÚ	HeavisideÚSÚasinhÚacoshÚatanhÚacothÚexpandÚFunctionÚjacobiÚ
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elliptic_eÚasecÚacscÚacot)ÚmanualintegrateÚfind_substitutionsÚ_parts_ruleÚintegral_stepsÚcontains_dont_knowÚmanual_subs)ÚraisesÚslowzx y z u n a b cÚfc                   C   sô   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s1J ‚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s[J ‚t tttd  ƒ ttƒtd  tddƒttƒfgksxJ ‚d S )Né   é   é   é   éÿÿÿÿ)	r?   r   Úxr   Úur   r   r	   r   © rN   rN   úC/usr/lib/python3/dist-packages/sympy/integrals/tests/test_manual.pyÚtest_find_substitutions   s   2(ÿ,ÿÿ>rP   c                   C   s0  t ttƒtt ksJ ‚t tdƒtƒttdƒ ksJ ‚t td tƒtd d ks)J ‚t dtd  dtd   tƒtd td  ksBJ ‚t td d tƒtd d d ksUJ ‚t dt d d tƒdt d d d kslJ ‚t td d tƒtd d d ksJ ‚t dt d d tƒdt d d d ks–J ‚d S )NrG   é   rJ   é	   )r>   ÚyrL   r	   rM   rN   rN   rN   rO   Ú test_manualintegrate_polynomials   s   2&.&2rT   c                   C   s¾   t tdt ƒtƒtdt ƒd ksJ ‚t dt tƒdt tdƒ ks$J ‚t dt tƒttƒks1J ‚t ddt d  tƒtdt d ƒd ksHJ ‚t ttƒd t tƒttƒd d ks]J ‚d S )NrG   rH   rQ   )r>   r	   rL   r   rN   rN   rN   rO   Ú!test_manualintegrate_exponentials%   s
   &"..rU   c                  C   sì  t ttƒttƒ tƒttƒttƒ d ttƒttƒ d  ks!J ‚t dt ttƒ tƒdt ttƒ dttƒ  ks<J ‚t tttƒ tƒtd ttƒ d td d  ksWJ ‚t ttƒtƒtttƒ t kshJ ‚t dtd  d ttƒ tƒdtd  ttƒ dt ttƒ  dttƒ  ks‘J ‚t ttƒtƒtttƒ ttd d ƒd  ksªJ ‚t tdt ƒtd  tƒ t¡s¼J ‚t	ttƒtƒd ksÇJ ‚t	ttƒtƒd ksÒJ ‚t	td tƒd ksÝJ ‚t	ttƒtƒ} | d ttƒkrò| d dksôJ ‚d S )	NrG   rJ   rQ   é   rI   é   rH   r   )
r>   r	   rL   r   r   r   r
   Úhasr   r@   )ÚresultrN   rN   rO   Útest_manualintegrate_parts.   s    &ÿ66".ÿ2$$rZ   c                   C   sL  t ttƒtƒttƒ ksJ ‚t ttƒtƒtttƒƒ ksJ ‚t ttƒtƒtttƒttƒ ƒks1J ‚t ttƒtƒtttƒttƒ ƒ ksEJ ‚t ttƒttƒ tƒttƒd d ttƒd  d fv scJ ‚t ttƒ ttƒ tƒttƒ ksvJ ‚t ttƒttƒ tƒttƒ ksˆJ ‚t ttƒd tƒttƒks—J ‚t ttƒd tƒttƒ ks§J ‚t tttd ƒ tƒtttd ƒttd ƒ ƒd ksÄJ ‚t ttƒtttƒƒ tƒttttƒƒtttƒƒ ƒ ksâJ ‚t tdt ƒttƒ tƒt tdt ƒ ksúJ ‚t tdt ƒttƒ tƒdtttƒƒ dtttƒd ƒ  dttƒd   ks$J ‚d S )NrG   rQ   éýÿÿÿ)	r>   r   rL   r   r   r   r   r   r   rN   rN   rN   rO   Ú!test_manualintegrate_trigonometryC   s    &(<&$ :<02ÿr\   c                   C   sæ  t ttƒd ttƒ tƒttƒd d ksJ ‚t ttƒd ttƒd  tƒtd tdt ƒd  ks4J ‚t ttƒttƒd  tƒttƒd  d ksLJ ‚t ttƒd ttƒd  tƒttƒd d ttƒd d  ksmJ ‚t ttƒd ttƒ tƒttƒd d ttƒ ksˆJ ‚t ttƒttƒd  tƒttƒd d ksŸJ ‚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sÅJ ‚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sñJ ‚d S )	NrG   rQ   é   rJ   é    rV   rI   é   )r>   r   rL   r   r   r   r   r   rN   rN   rN   rO   Útest_manualintegrate_trigpowersW   s    .ÿ0ÿ6.,ÿ4ÿr`   c                  C   s~  t ttƒdtdt ƒ  tƒtttƒƒksJ ‚t dddtd    tƒtdt d ƒd ks0J ‚t dddtd    tƒttƒd ksEJ ‚t ddtd   tƒttd ƒd ksZJ ‚t dddtd    tƒtdt ƒd ksqJ ‚tdd	d
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   ksZJ ‚t ttƒtƒtttƒ ttd d ƒd  kstJ ‚t tt
t ƒtƒtt
t tt
t ƒ tt
d td  d ƒd  t
 tt
dƒftt d d	fƒks¨J ‚t ttt
t ƒ tƒt
tt
d  tttt
d ƒ ƒt
d tt
d ƒ    d td tt
t ƒ d  ksàJ ‚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sOJ ‚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s½J ‚d S )NrH   rG   rJ   rR   rQ   rI   é   ÚaT©ÚrealÚbr   rK   éüÿÿÿ)r   Téþÿÿÿ)r>   r	   rL   r
   r   r   r   r!   r   r    rb   re   r   r   r   r   r   r   r   r   r   r<   r;   r=   )ÚraÚrbrN   rN   rO   Ú test_manualintegrate_inversetrigi   sÂ   .2**.0HHþÿ8JJþ
ÿ,DDþ
ÿ,D(00:
ÿ

ÿ

ÿ
ÿJ
ÿ8
ÿ
ÿ

ÿ

ÿ
ÿ*
ÿL
ÿ0Zf0fd4\rBVbBVb4hp<><þ
ÿ>8>þÿrj   c                	   C   s”  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tddƒk ttddƒkƒfƒks6J ‚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sxJ ‚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sÈJ ‚d S )Nra   rG   rR   rQ   rJ   r[   rH   é   é}   é   rV   éûÿÿÿr_   é1   iÅÑ·iÁöW )	r>   r   rL   r   r   r   r   r   ZHalfrN   rN   rN   rO   Ú&test_manualintegrate_trig_substitutionÊ   s*   (ÿÿ  &ÿÿÿ&ÿþþÿrp   c                  C   sˆ   t ttƒtt ƒ t tƒtt ƒ ttƒ ksJ ‚tdƒ} t | tƒ| t ƒ t tƒt| t ƒt tƒ t| tƒt tƒ ksBJ ‚d S )NrF   )r>   r	   rL   r.   r#   r   ©rF   rN   rN   rO   Ú)test_manualintegrate_trivial_substitutionÖ   s
   4&ÿrr   c                   C   s    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s*J ‚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sNJ ‚d S )NrH   rJ   rG   rK   )r>   rL   r   r!   r    rN   rN   rN   rO   Útest_manualintegrate_rationalÜ   s   TLrs   c                  C   sØ  dt td  d ƒ dtdƒ ttƒ ttdƒt d ƒ } }t| tƒ|kr/| t¡ | ¡s1J ‚dt dtd  ƒ dttƒ tdt ƒ d } }t| tƒ|krY| t¡ | ¡s[J ‚tt	ddƒ t t d ƒ dt
t	ddƒtd ƒ } }t| tƒ|kr…| t¡ | ¡s‡J ‚t dt ƒt tdt ƒ} }t| tƒ|kr¥| t¡ | ¡s§J ‚t ddt  td  ƒttƒt dƒ ttd ƒ d } }t| tƒ|krÓ| t¡ | ¡sÕJ ‚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)| t¡ | ¡s+J ‚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]| t¡ | ¡s_J ‚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| t¡ | ¡s‘J ‚tdt d ƒt tdƒ tdt ƒ tdƒtdt ƒ  } }t| tƒ|krÂ| t¡ | ¡sÄJ ‚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rú| t¡ | ¡süJ ‚ttd ƒt ttd ƒ} }t| tƒ|kr| t¡ | ¡sJ ‚ttd ƒt ttd ƒd } }t| tƒ|kr@| t¡ | ¡sBJ ‚dtdt d ƒ tdt d ƒd } }t| tƒ|krh| t¡ | ¡sjJ ‚tddt ƒt tddt ƒ} }t| tƒ|krŒ| t¡ | ¡sŽJ ‚dtddttƒd   ƒ dtdƒ ttt	ddƒƒ d } }t| tƒ|kr¾| t¡ | ¡sÀJ ‚tddttƒd   ƒdttt	d	dƒƒ } }t| tƒ|krè| t¡ | ¡sêJ ‚d S )
NrJ   rG   rQ   rH   r]   iðÿÿÿrV   rR   i÷ÿÿÿ)r	   rL   r   r   r   r>   r   Úequalsr6   r   r,   r.   r   r4   r   r3   r/   r0   r7   r1   r8   r2   r   r-   r5   r9   r:   ©rF   ÚFrN   rN   rO   Útest_manualintegrate_specialà   sJ   @"2"6"":":*ÿÿ&B&>&@&J&&"&*&"&>&.*rw   c                   C   s´   t tttd dt  d ƒ tƒttd dt  d  ksJ ‚t ttd dt  d tƒtƒtttd dt  d tƒƒks@J ‚t tttƒttttƒtƒtttƒtttƒksXJ ‚d S )NrG   rQ   )r>   r   r   rL   rS   r   r   rN   rN   rN   rO   Útest_manualintegrate_derivative  s    ÿÿÿrx   c                  C   s*  t ttƒtƒtttƒ ksJ ‚t ttdƒ tƒtd d ks J ‚t ttdƒ tƒdks-J ‚t tttƒ tƒtd ttƒ d ksBJ ‚t ttt ƒ tƒtd tt ƒ d ksYJ ‚t tdt d ƒtƒtd tdt d ƒ ksrJ ‚t tttƒ tƒtd ttƒ d ks‡J ‚t ttd ƒtdt ƒ td  tƒtd d tddƒ ttd ƒ tddƒ tt d ƒ ks¹J ‚tdƒ} t tdt ƒtdt d ƒ tƒttd ƒ ttd	dƒƒ tdt tdƒ ƒ ksèJ ‚t t| t ƒtdt |  ƒ tƒt| tddƒ ƒtt|  ƒ tdt |  ƒ ksJ ‚d S )
NrG   rg   r   rJ   rH   rQ   rS   r_   é   )r>   r   rL   r   r   r   r   r   )rS   rN   rN   rO   Útest_manualintegrate_Heaviside  s"   "*.2*$8ÿ .ÿ ,ÿrz   c                  C   sn  t dƒ} dtddƒ}}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}|D ]€}t|tƒ}dD ]%}z| | |¡}W n	 tyP   Y q=w | | |¡ t¡|  ¡ dksbJ ‚q=t| tdt d ¡ }t|tƒ}d	D ]}| | |¡ t¡| | |¡  ¡ dksJ ‚qvt d
ƒ}	tt|jƒd ƒD ]}
t|jƒ}|	||
< tt|j|Ž |	ƒtƒs³J ‚q›q4d S )NÚnr_   rV   rQ   )rg   rK   r   rH   rQ   rV   r]   r   rG   rH   )rG   rJ   r_   Út)r   r   r$   rL   r%   r&   r'   r(   r)   r*   r+   r>   ZsubsÚ
ValueErrorr   r"   ÚrangeÚlenÚargsÚlistÚ
isinstanceÚfuncr   )r{   rb   re   ZpolysÚpZintegralZdegZp_subbedÚqr|   ÚiÚnew_argsrN   rN   rO   Ú$test_manualintegrate_orthogonal_poly!  s4    
þ
ÿ$
,
ýîrˆ   c                  C   sê   t td ¡ ƒ\} }}tdddd}t|||  ƒt|| ƒ }|t tf}t||ƒ|| d td| | ƒd  t|| ƒ t|| ƒt|| ƒd  d  | ksTJ ‚| t||ƒ ¡  t | t|| ƒ ksiJ ‚t||ƒ 	t
¡rsJ ‚d S )Nzr x phir{   T)ZintegerÚpositiverG   rJ   )Úmapr   Úsplitr   r   r>   r   r   ZtrigsimprX   r   )ÚrrL   Zphir{   Z	integrandZlimitsrN   rN   rO   Útest_issue_6799?  s   Nÿ*r   c                   C   sB   t tt tƒtttd  td  ttdƒfttƒdfƒksJ ‚d S )NrH   rK   T)r>   rL   rS   r   r   r   rN   rN   rN   rO   Útest_issue_12251L  s   &ÿrŽ   c                   C   sr   t ttttd  ƒƒtƒtttd  ƒksJ ‚ttttd ƒ tddt ttƒ tttd  ƒ d ks7J ‚d S )NrG   rJ   F)Zrisch)	r>   r   r	   rL   r   r   r   r   r   rN   rN   rN   rO   Útest_issue_3796Q  s   .Dr   c                   C   sŠ   t ttƒttƒ tddttƒttƒ d ttƒttƒ d  ks#J ‚t ttƒttƒ tddttƒd d ttƒd  d fv sCJ ‚d S )NT)ZmanualrG   )r   r	   rL   r   r   rN   rN   rN   rO   Útest_manual_trueV  s   &ÿ ÿr   c               
   C   s  t dƒ} t dƒ}t| t tƒt| t t| ƒ tt| ƒdƒftdfƒks%J ‚t| |t  tƒtt| |t  t| ƒ tt| ƒdƒf|t dfƒ| t|dƒftdfƒksTJ ‚tt|t ƒtƒtt|t ƒ| t|dƒftdfƒksqJ ‚t ddd} t| d t tƒ| d t t| d ƒ ksŽJ ‚t ddd} t| d t tƒtks¡J ‚t dƒ} t ddd}t| |t  tƒt| |t  t| ƒ tt| ƒdƒf|t dfƒ| ksÐJ ‚t ddd} t| d |t  tƒ| d |t  |t| d ƒ  ksóJ ‚t d	dd
}t dƒ}td||td    tƒttt|| ƒ ƒ|t|| ƒ  ksJ ‚t ddd
}td||td    tƒttt| ƒtd| ƒ  ƒ|t| ƒ td| ƒ  ksQJ ‚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s®J ‚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sÛJ ‚tdt|t  t|d    tƒt	d|t  |d t  t  tƒksJ ‚d S )NrS   r{   r   T)r‰   rH   )Zzero)Znonzerorb   )Únegativere   rG   rK   rJ   )
r   r>   rL   r   r   r   r	   r
   r   r   )rS   r{   rb   re   rN   rN   rO   Útest_issue_6746]  sp   "
ÿ 
þýý
û
ÿ.*ÿ
ÿÿD6
ÿ0.ÿ*ÿÿ
ÿ((
ÿ "ÿr’   c                   C   s~  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>J ‚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|J ‚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s½J ‚d S )NrG   rH   )r>   r   rL   r   r   r   r   r
   rN   rN   rN   rO   Útest_issue_2850…  s&   2$ÿ
ÿ2$ÿ
ÿ*ÿÿÿÿr“   c                	   C   s  t tdt ƒttƒ tƒttƒtdt ƒ d dttƒ tdt ƒ d  ks)J ‚tttdt ƒttƒ tƒƒr:J ‚t td td dt  d d  tƒtttd dtd   dtd   dt  d  tƒdtdtd dtd   dtd   dt  d  tƒ  ks‡J ‚d S )NrG   rV   rQ   rJ   r]   rH   )r>   r   rL   r	   r   rB   rA   r   rN   rN   rN   rO   Útest_issue_9462  s   R"$48ÿÿr”   c                  C   s  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r4| t¡| ks6J ‚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rŠ| t¡| ksŒJ ‚d S )NrJ   ra   é   é€   é!  éð   )r   rL   r	   r   r>   r   ru   rN   rN   rO   Útest_cyclic_parts—  s   8 :ÿÿ$r™   c                   C   s¾   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s]J ‚d S )
NrJ   rQ   ra   rG   é   r]   rI   rV   rH   )r>   rL   r
   rN   rN   rN   rO   Útest_issue_10847_slow¡  s   0Bÿÿ:þr›   c                  C   sÐ  t td td t  tƒttttt ƒ ƒ tt ƒ t ks!J ‚tddd} t 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 t ksJ ‚t ttt
 ƒttt ƒ tƒdt
tddƒ  tttt
 ƒtt
ƒ ƒ d dt
 ttt
 ƒ d  dtt
 tddƒ  ttt ƒ d  dtt
 tddƒ  d  ksÓJ ‚td	dd}td
dd}t tt| ƒt|t ƒ tƒd|d  tttt| ƒt|ƒ ƒt|ƒ |dkfttt| ƒt| ƒ ƒ t| ƒ tt| | k|dk ƒft	tt| ƒt| ƒ ƒ t| ƒ tt| | k |dk ƒfƒ d d| tt| ƒ d  dt| tddƒ  t|t ƒ d  dt| tddƒ  d  kswJ ‚t ttƒttƒ tƒdttddƒ  ttƒ d dttddƒ  d  ksŸJ ‚t ttt t ƒt tƒdt tttt t ƒtt ƒ ƒ tt ƒ dttt t ƒ  ksÑJ ‚tddd}tddd}t t|t | ƒt tƒd| ttt|t | ƒt| ƒ ƒ t| ƒ | dkftt|t | ƒt|ƒ ƒt|ƒ t| dk |t | |kƒft	t|t | ƒt|ƒ ƒt|ƒ t| dk |t | |k ƒfƒ dt|t | ƒ  ksUJ ‚tt t|t | ƒt|   tƒƒd| |  ttt|t | ƒt||  | ƒ ƒt||  | ƒ ||  | dkftt|t | ƒt| |  | ƒ ƒ t| |  | ƒ t||  | dk |t | | |  | kƒft	t|t | ƒt| |  | ƒ ƒ t| |  | ƒ t||  | dk |t | | |  | k ƒfƒ d| ttt|t | ƒt||  | ƒ ƒt||  | ƒ ||  | dkftt|t | ƒt| |  | ƒ ƒ t| |  | ƒ t||  | dk |t | | |  | kƒft	t|t | ƒt| |  | ƒ ƒ t| |  | ƒ t||  | dk |t | | |  | k ƒfƒ  dt|t | ƒ  ksJ ‚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sÁJ ‚t tdt d ƒd t tƒdt d tddƒ d dt d tddƒ d  ksíJ ‚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J ‚t td ttƒ tƒttƒ dtd   ddtd    ks9J ‚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sfJ ‚d S )NrG   ÚcTrc   r   rJ   rQ   rR   rS   Úzrb   re   rg   rH   rV   é   rk   r[   rK   )r>   rL   rœ   r
   r   r   r   r!   r   r    rS   r   r   r   rb   re   r"   r   )ZrcZryZrzrh   ri   rN   rN   rO   Útest_issue_10847¨  s†   B(00þþÿD$ÿÿÿ2<<þþý$ýü
ÿPB
ÿ:>>þý
ÿ^ÿddþJddþýûhXVB 0ÿrŸ   c                   C   sd   t tttƒ t¡tƒtttttƒtƒtƒksJ ‚t tttƒ t¡ t¡tƒttttƒtƒks0J ‚d S ©N)r>   rF   rL   rS   r   r   r   rN   rN   rN   rO   Útest_issue_12899Ù  s   04r¡   c                   C   s2   t tttddfƒtƒttttddfƒ ksJ ‚d S )NrH   rG   )r>   r   rS   rL   rN   rN   rN   rO   Ú#test_constant_independent_of_symbolÞ  s   ÿr¢   c                   C   s´   t tdt ƒtƒtdt ƒ d ksJ ‚t ttƒtdt ƒ tƒdttƒd  d ks-J ‚t tdt ƒttƒ dttƒ  tƒdtttƒd ƒ ttƒd  dttƒ  ksXJ ‚d S )NrG   rg   rQ   rH   )r>   r   rL   r   r   rN   rN   rN   rO   Útest_issue_12641ã  s
   (2$*ÿr£   c                   C   s4   t ttƒttƒd  tƒttƒd  d ksJ ‚d S )NrV   rI   )r>   r   rL   r   rN   rN   rN   rO   Útest_issue_13297ê  s   4r¤   c                   C   sR   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s'J ‚d S )NrH   rK   )r>   rL   r   r   rN   rN   rN   rO   Útest_issue_14470ï  s   .ÿr¥   c                  C   sÐ  t ttƒtttƒƒ tƒtttƒƒksJ ‚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s6J ‚t tdt ƒtttƒƒ tƒ} |  t¡rLJ ‚|  t¡tdt ƒtttƒƒ ks_J ‚t tdd„ t	ddƒD ƒ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sæJ ‚d S )NrG   é
   c                 S   s   g | ]
}t t|t  ƒ ‘qS rN   )rL   r	   )Ú.0ÚkrN   rN   rO   Ú
<listcomp>ý  s    z#test_issue_9858.<locals>.<listcomp>rH   r]   r_   rI   rV   rJ   rQ   ro   é$   rk   ra   rR   )
r>   r	   rL   r   r   rX   r   r   Úsumr~   )ÚresrN   rN   rO   Útest_issue_9858ô  s<   *ÿ&Nÿÿ
ÿÿÿþþþþþÿr­   c                  C   s”   t ttd d  tƒttd ƒd ksJ ‚t td td d  tƒttd d ƒd ks.J ‚td	td  d d  } t | tƒ t¡ ¡ | ksHJ ‚d S )
NrJ   rH   rG   rI   rk   rQ   rV   rm   rR   )r>   rL   r
   r   Zfactorrq   rN   rN   rO   Útest_issue_8520  s   *2 r®   c                      sŽ   t dƒ\‰‰tˆƒtˆƒ ‰ tˆ tˆƒˆƒˆttˆƒƒ ks J ‚tˆ tˆƒˆƒtˆƒˆ ks0J ‚tt‡ ‡fdd„ƒ tt‡ ‡‡fdd„ƒ d S )Nzx yc                      s
   t ˆ ˆƒS r    )rC   rN   )ÚexprrL   rN   rO   Ú<lambda>  s   
 z"test_manual_subs.<locals>.<lambda>c                      s   t ˆ tˆƒˆˆƒS r    )rC   r	   rN   ©r¯   rL   rS   rN   rO   r°     s    )r   r   r	   rC   rD   r}   rN   rN   r±   rO   Útest_manual_subs
  s   $ r²   c                  C   sØ   t tƒtt tƒƒ ttddƒ  } dttddƒ  tt tƒƒ d dttddƒ  tt tƒƒ d  dttddƒ  tt tƒƒ d dttddƒ  tt tƒƒ d  t tƒ  }t| tƒ|krh| t¡ | ¡sjJ ‚d S )	NrQ   rJ   i€ÿÿÿrH   r—   r˜   ra   r•   )r   rL   r   r   r   r>   r   rt   ru   rN   rN   rO   Útest_issue_15471  s   "&r³   c               	   C   sÞ   dt  d dt d  dt   d  } t| t ƒdtdt d  dt   d ƒ d dtdƒ tdtdƒ t tddƒ  d ƒ d	  ksDJ ‚ddt d  dt   d  }t|t ƒdtd
t  d ƒ dtd
t  d
 ƒ  ksmJ ‚d S )NrV   rG   rQ   r]   rI   rW   é   rH   éE   rJ   )rL   r>   r   r   r
   r   )rF   ÚgrN   rN   rO   Útest_quadratic_denom  s   $d:r·   N)rZsympyr   r   r   r   r   r   r   r	   r
   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r   r    r!   r"   r#   r$   r%   r&   r'   r(   r)   r*   r+   r,   r-   r.   r/   r0   r1   r2   r3   r4   r5   r6   r7   r8   r9   r:   r;   r<   r=   Zsympy.integrals.manualintegrater>   r?   r@   rA   rB   rC   Zsympy.testing.pytestrD   rE   rL   rS   r   rM   r{   rb   re   rœ   rF   rP   rT   rU   rZ   r\   r`   rj   rp   rr   rs   rw   rx   rz   rˆ   r   rŽ   r   r   r’   r“   r”   r™   r›   rŸ   r¡   r¢   r£   r¤   r¥   r­   r®   r²   r³   r·   rN   rN   rN   rO   Ú<module>   s`   ø  	

`%	
(
	


0


