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 Cosh

 http://functions.wolfram.com/01.20.21.1235.01

 Input Form

 Integrate[(Sin[e z]^m Cosh[c z])/(a + b E^(d z))^n, z] == (1/c) ((2^(-1 - m) Binomial[m, m/2] ((-E^((-c) z)) Hypergeometric2F1[-(c/d), n, (-c + d)/d, -((b E^(d z))/a)] + E^(c z) Hypergeometric2F1[c/d, n, (c + d)/d, -((b E^(d z))/a)]) (1 - Mod[m, 2]))/a^n) + (2^(-1 - m) Sum[(-1)^k Binomial[m, k] (Cos[(m Pi)/2] ((E^((c + 2 I e k - I e m) z) Hypergeometric2F1[ (c + 2 I e k - I e m)/d, n, (c + d + 2 I e k - I e m)/d, -((b E^(d z))/a)] - E^((-c - 2 I e k + I e m) z) Hypergeometric2F1[(-c - 2 I e k + I e m)/d, n, (-c + d - 2 I e k + I e m)/d, -((b E^(d z))/a)])/ (c + 2 I e k - I e m) + (E^((-c + 2 I e k - I e m) z) Hypergeometric2F1[(-c + 2 I e k - I e m)/d, n, (-c + d + 2 I e k - I e m)/d, -((b E^(d z))/a)] - E^((c - 2 I e k + I e m) z) Hypergeometric2F1[(c - 2 I e k + I e m)/d, n, (c + d - 2 I e k + I e m)/d, -((b E^(d z))/a)])/ (-c + 2 I e k - I e m)) + I ((E^((c + 2 I e k - I e m) z) Hypergeometric2F1[(c + 2 I e k - I e m)/d, n, (c + d + 2 I e k - I e m)/d, -((b E^(d z))/a)] + E^((-c - 2 I e k + I e m) z) Hypergeometric2F1[(-c - 2 I e k + I e m)/d, n, (-c + d - 2 I e k + I e m)/d, -((b E^(d z))/a)])/ (c + 2 I e k - I e m) + (E^((-c + 2 I e k - I e m) z) Hypergeometric2F1[(-c + 2 I e k - I e m)/d, n, (-c + d + 2 I e k - I e m)/d, -((b E^(d z))/a)] + E^((c - 2 I e k + I e m) z) Hypergeometric2F1[(c - 2 I e k + I e m)/d, n, (c + d - 2 I e k + I e m)/d, -((b E^(d z))/a)])/ (-c + 2 I e k - I e m)) Sin[(m Pi)/2]), {k, 0, Floor[(1/2) (-1 + m)]}])/a^n /; Element[n, Integers] && n > 0 && Element[m, Integers] && m > 0

 Standard Form

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 MathML Form

 Rule Form

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

 2002-12-18