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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function and exponential function > Involving products of powers of two direct functions and exponential function > Involving product of power of the direct function, the direct function and exponential function > Involving ep zr sin(b zr)sinv(c zr)





http://functions.wolfram.com/01.06.21.1392.01









  


  










Input Form





Integrate[E^(p z^r) Sin[b z^r] Sin[c z^r]^v, z] == (1/r) (2^(-1 - v) z (I Binomial[v, v/2] (Gamma[1/r, ((-I) b - p) z^r]/ (((-I) b - p) z^r)^r^(-1) - Gamma[1/r, I (b + I p) z^r]/ (I (b + I p) z^r)^r^(-1)) (1 - Mod[v, 2]) + I^(-v - 1) Sum[(-1)^s Binomial[v, s] (((-(-1)^v) Gamma[1/r, (-I) (b - I p + 2 c s - c v) z^r])/ ((-I) (b - I p + 2 c s - c v) z^r)^r^(-1) + Gamma[1/r, I (b + I p + 2 c s - c v) z^r]/ (I (b + I p + 2 c s - c v) z^r)^r^(-1) - Gamma[1/r, (-I) (b - I p - 2 c s + c v) z^r]/ ((-I) (b - I p - 2 c s + c v) z^r)^r^(-1) + ((-1)^v Gamma[1/r, I (b + I p - 2 c s + c v) z^r])/ (I (b + I p - 2 c s + c v) z^r)^r^(-1)), {s, 0, Floor[(1/2) (-1 + v)]}])) /; Element[v, Integers] && v > 0










Standard Form





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MathML Form







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<apply> <times /> <imaginaryi /> <ci> p </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> </apply> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> b </ci> <apply> <times /> <imaginaryi /> <ci> p </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> s </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> c </ci> <ci> v </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> r 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18