
    \h                     t    S SK JrJrJr  S SKJrJrJrJrJ	r	J
r
JrJr  S SKJr  \" S5      rS rS rS rS rg	)
    )NeRationalSymbol)sincostancscseccotlog	Piecewise)trigintegratexc            	         [        [        S5      [        5      [        :X  d   e[        [        [        5      b   e[        [        S-  [        5      b   e[        [        [        5      [        5      [	        [        5      * :X  d   e[        [	        [        5      [        5      [        [        5      :X  d   e[        [        S[        -  5      [        5      [	        S[        -  5      * S-  :X  d   e[        [	        S[        -  5      [        5      [        S[        -  5      S-  :X  d   e[        S5      n [        [        U [        -  5      [        5      [        [	        U [        -  5      * U -  [        U S5      4S5      :X  d   e[        [	        U [        -  5      [        5      [        [        U [        -  5      U -  [        U S5      4[        S45      :X  d   e[        [        U [        -  5      S-  [        5      [        [        U -  S-  [        [        U -  5      [	        [        U -  5      -  S-  -
  U -  [        U S5      4S5      :X  d   e[        [        U [        -  5      [	        U [        -  5      -  [        5      [        [        [        U -  5      S-  SU -  -  [        U S5      4S5      :X  d   e[        [	        U [        -  5      S-  [        5      [        [        U -  S-  [        [        U -  5      [	        [        U -  5      -  S-  -   U -  [        U S5      4[        S45      :X  d   e[        SSS9n [        [        U [        -  5      [        S	S
9[	        U [        -  5      * U -  :X  d   e[        [	        U [        -  5      [        S	S
9[        U [        -  5      U -  :X  d   e[        [        [        5      [	        [        5      -  [        5      [        [        5      S-  S-  :X  d   e[        [        [        5      [	        [        5      S-  -  [        5      [	        [        5      S-  * S-  :X  d   e[        [        [        5      S-  [	        [        5      -  [        5      [        [        5      S-  S-  :X  d   e[        [        [        5      S-  [	        [        5      -  [        5      [        [        5      S-  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      S-  -  [        5      [	        [        5      S-  S-  [	        [        5      S-  S-  -
  :X  d   e[        [        [        5      S-  [	        [        5      S-  -  [        5      [        [        [        5      S-  S-
  5      * S-  [        [        [        5      5      -   :X  d   eg )N         yr   )r   TT)positivenone)conds      
   )	r   r   r   r   r   r   r   r   r   )r   s    _/var/www/auris/envauris/lib/python3.13/site-packages/sympy/integrals/tests/test_trigonometry.pytest_trigintegrate_oddr      s   !a(A---A&&&Aq!)))Q#Aw...Q#s1v---QqS1%#ac(1444QqS1%QqS!333sAQqS1%
ac(1bAh*, , , ,QqS1%	QqS!R1XD	*+ + + +QqS1a(I
A#a%#ac(3qs8#A%
%q	("Q(3Y-@ @ @ @QqS#ac(*A.)	QqS1ac	Bq!H%y32 2 2 2QqS1a(I
A#a%#ac(3qs8#A%
%q	("Q(3aY-@ @ @ @ 	sT"A QqS1F3AaCy{BBBQqS1F3s1Q3xzAAAQA*c!faik999QA	)1-#a&!)A===Q3q6)1-Q1<<< QSV+Q/3q619Q;>>>Q#a&!)+Q/CFAI:a<???QSVQY.2	QBQ1$% % %QSVQY.2A
2A	!#$ $ $ QCFBJ.2	SVQY]	ACF+, , ,    c                  D   [        [        [        5      S-  [        5      [        S-  [        [        5      [        [        5      -  S-  -
  :X  d   e[        [        [        5      S-  [        5      [        S-  [        [        5      [        [        5      -  S-  -   :X  d   e[        [        S[        -  5      S-  [        5      [        S-  [        S[        -  5      [        S[        -  5      -  S-  -
  :X  d   e[        [        S[        -  5      S-  [        5      [        S-  [        S[        -  5      [        S[        -  5      -  S-  -   :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        S-  [        S[        -  5      [        S[        -  5      -  S-  -
  :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        S-  [        [        5      [        [        5      -  S-  -
  [        [        5      S-  [        [        5      -  S-  -
  [        [        5      S-  [        [        5      -  S-  -   :X  d   e[        [        [        5      S-  [        [        5      S-  -  [        5      [        S-  [        [        5      [        [        5      -  S-  -   [        [        5      S-  [        [        5      -  S-  -   [        [        5      S-  [        [        5      -  S-  -
  :X  d   e[        [        [        5      S	-  [        5      S
[        [        5      -  S[        [        5      -  -  [        [        5      S[        [        5      S-  -  -  -
  :X  d   e[        [        [        5      S-  [        5      [        [        5      S[        [        5      S-  -  -  S[        [        5      -  S[        [        5      S-  -  -  -   S[        [        5      -  S[        [        5      -  -  -   :X  d   eg )Nr   r      r               i   )r   r   r   r    r   r   test_trigintegrate_evenr)   9   s%   QA&!A#As1va*????QA&!A#As1va*????QqS1a(AaC#ac(3qs82CA2E,EEEEQqS1a(AaC#ac(3qs82CA2E,EEEEQSVQY.2	!c!A#hs1Q3x""# # # QSVQY.2	"s1vs1v~b  3q619SV#3B#66A	#a&	   QSVQY.2	"s1vs1v~b  3q619SV#3B#66A	#a&	   Q"q)RAY#a&-A
a&!CFAI+
.    Q"q)SVQs1vqy[-A
CF(Bs1vqyL
!."$%c!fHbQi$8.9 9 9 9r   c                     [        [        [        5      [        [        5      -  [        5      [	        [        [        5      5      * :X  d   e[        [        [        5      [        [        5      -  [        5      [        :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      :X  d   e[        [        [        5      [        [        5      -  [        5      [        :X  d   e[        [        [        5      [        [        5      -  [        5      [	        [        [        5      5      :X  d   e[        [        [        5      [        [        5      -  [        5      [        [        5      * :X  d   e[        [        [        5      [        [        5      -  [        5      [	        [        [        5      S-
  5      S-  [	        [        [        5      S-   5      S-  -
  [        [        5      -   :X  d   e[        [        [        5      [        [        5      S-  -  [        5      [	        [        [        5      5      [        [        5      S-  S-  -
  :X  d   eg )Nr   r   )	r   r   r   r
   r   r   r	   r   r   r(   r   r   test_trigintegrate_mixedr+   Q   s   QA*s3q6{l:::QA*a///QA*c!f444QA*a///QA*c#a&k999QA*s1vg555QA*c#a&1*oa.?
c!fqj/!
/!!f/% % % %QA	)1-SVs1vqy{1JJJJr   c                      [        SSS9n [        [        [        5      U -  [        5      b   e[        [	        [        5      U -  [        5      b   e[        [        [        5      U -  [        5      b   eg )NnT)integer)r   r   r   r   r   r   )r-   s    r   test_trigintegrate_symbolicr/   ^   s_    sD!AQA&...QA&...QA&...r   N)
sympy.corer   r   r   sympy.functionsr   r   r   r	   r
   r   r   r   sympy.integrals.trigonometryr   r   r   r)   r+   r/   r(   r   r   <module>r3      s6    + + H H H 6
3K.,b90
K/r   