K iK+ddlmZmZmZmZmZmZmZddlm Z m Z m Z m Z m Z ddlmZdZedZedZd dZd Zd Zy ) )cacheitDummyNeIntegerRationalSWild)binomialsincos PiecewiseAbs) integratec"t|tS)N) isinstancer)ns b/mnt/ssd/data/python-lab/Trading/venv/lib/python3.12/site-packages/sympy/integrals/trigonometry.py_integer_instancers a !!ctd|g}dDcgc]}t||gtgc}\}}t||z|zt||z|zz}||||fScc}w)Na)excludenm)r properties)r rr r )xrsrmpats r _pat_sincosr sp S1#A  QC->,? @ DAq ac(A+AaC! #C 1a< sAuc t|\}}}}|jd}|j|}|y||||}}|jr|jr|S|jr|ntj }||}|j s |j rt} |j |j } } | rA| r?|dkr |dkDrd} d} n0|dkr |dkDrd} d} n!|dkr|dkr ||kD} ||kD } n ||k} ||k } | r'd| dzz |dz dz z | |zz} t||z} n'| r%| |zd| dzz |dz dz zz} t||z} t | }|j|  }|dk(rt||z t|df|dfS||z St|t|kD} t|t|kD} tj }| r|dkDrRtd|dzdzD];}|tj |zt#|dz|zt%|d|zz|zz }=n|dk(rt%||}n~t'd |dzt||dzzzt||dz zzt'|dz |dzt)t||dzzt||dz zz|zz}n| r|dkDrRtd|dzdzD];}|tj |zt#|dz|zt+|d|zz|zz }=n|dk(rt+||}nt'd|dzt||dz zzt||dzzzt'|dz |dzt)t||dz zt||dzzz|zz}n&||k(r-ttd|ztj,z|z|}n|| k(r|dkrut'd|dzt||dz zzt||dzzzt'|dz |dztt||dz zt||dzzz|zz}ntt'd |dzt||dzzzt||dz zzt'|dz |dztt||dzzt||dz zz|zz}|dk(r0t|j|||z|z t|df|dfS|j|||z|z S) a Integrate f = Mul(trig) over x. Examples ======== >>> from sympy import sin, cos, tan, sec >>> from sympy.integrals.trigonometry import trigintegrate >>> from sympy.abc import x >>> trigintegrate(sin(x)*cos(x), x) sin(x)**2/2 >>> trigintegrate(sin(x)**2, x) x/2 - sin(x)*cos(x)/2 >>> trigintegrate(tan(x)*sec(x), x) 1/cos(x) >>> trigintegrate(sin(x)*tan(x), x) -log(sin(x) - 1)/2 + log(sin(x) + 1)/2 - sin(x) References ========== .. [1] https://en.wikibooks.org/wiki/Calculus/Integration_techniques See Also ======== sympy.integrals.integrals.Integral.doit sympy.integrals.integrals.Integral sincosNrTFr piecewise)r rewritematchis_zerorZerois_odd_ur r rsubsr rrrange NegativeOner _sin_pow_integrater trigintegrate_cos_pow_integrateHalf)frcondsrrrrMzzr!n_m_ffuufifxresis rr1r1s]Dq>LCAq (A  Ay Q41qAyyQYYiiQVVB !Axx188 188B "1uQQ1q5a%AEUa%[!ea%[ q!t8Aqy))AqD0BQqSBAQTa!eQY//BQqSB r1  WWQ^ K b1fbAh/"d< <Av " a&3q6/B a&3q6/B &&C  q51adQh' 8 q(8AqD!+<<*1qs7A678 8!V$Q*C&BA&Q!a%83q6AE?JAE1q5) Q!a%Q!a%!@!DEEC  q51adQh' 8 q(8AqD!+<<*1qs7A678 8!V%Q*C&Aq1u%AQ7AQGAE1q5) Q!a%Q!a%!@!DEEC 6S1Xaff_q0!4CA2g1u  1q5)CFQUO;c!fq1uoMAq1u- Q!a%3q6AE?!BAFGG AE*SVa!e_QA&);AE1)EEF G rN)r%) sympy.corerrrrrrr sympy.functionsr r r r r integralsrrr r,r1r0r2rrrGsMEEE>> "   3Z[ |*Z'r