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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving powers of cos and exp > Involving eb zr+e cosm(a zr+q) sinh(c zr+g)





http://functions.wolfram.com/01.19.21.1306.01









  


  










Input Form





Integrate[E^(b z^r + e) Cos[a z^r + q]^m Sinh[c z^r + g], z] == (-((I 2^(-1 - m) z)/r)) (Binomial[m, m/2] ((E^(e + g - (I Pi)/2) Gamma[1/r, (-b - c) z^r])/ ((-b - c) z^r)^r^(-1) + (E^(e - g + (I Pi)/2) Gamma[1/r, (-b + c) z^r])/((-b + c) z^r)^r^(-1)) (1 - Mod[m, 2]) + Sum[Binomial[m, s] ((E^(e + g - (I Pi)/2 - I m q + 2 I q s) Gamma[1/r, (-b - c + I a m - 2 I a s) z^r])/ ((-b - c + I a m - 2 I a s) z^r)^r^(-1) + (E^(e - g + (I Pi)/2 - I m q + 2 I q s) Gamma[1/r, (-b + c + I a m - 2 I a s) z^r])/((-b + c + I a m - 2 I a s) z^r)^ r^(-1) + (E^(e + g - (I Pi)/2 + I m q - 2 I q s) Gamma[1/r, (-b - c - I a m + 2 I a s) z^r])/ ((-b - c - I a m + 2 I a s) z^r)^r^(-1) + (E^(e - g + (I Pi)/2 + I m q - 2 I q s) Gamma[1/r, (-b + c - I a m + 2 I a s) z^r])/((-b + c - I a m + 2 I a s) z^r)^ r^(-1)), {s, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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





2002-12-18