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 Cosh

 http://functions.wolfram.com/01.20.21.3757.01

 Input Form

 Integrate[E^(p z) (a + b E^(d z))^\[Beta] Sin[e z] Cosh[c z]^v, z] == ((-2^(-1 - v)) I (a + b E^(d z))^\[Beta] Binomial[v, v/2] (E^(((-I) e + p) z) (I e + p) Hypergeometric2F1[((-I) e + p)/d, -\[Beta], (d - I e + p)/d, -((b E^(d z))/a)] + E^((I e + p) z) (I e - p) Hypergeometric2F1[(I e + p)/d, -\[Beta], (d + I e + p)/d, -((b E^(d z))/a)]) (1 - Mod[v, 2]))/ (1 + (b E^(d z))/a)^\[Beta]/((I e - p) (I e + p)) + (2^(-1 - v) I (a + b E^(d z))^\[Beta] Sum[Binomial[v, s] ((E^((I e + p + 2 c s - c v) z) ((-I) e + p - 2 c s + c v) Hypergeometric2F1[(I e + p + 2 c s - c v)/d, -\[Beta], (d + I e + p + 2 c s - c v)/d, -((b E^(d z))/a)] + E^(((-I) e + p - 2 c s + c v) z) ((-I) e - p - 2 c s + c v) Hypergeometric2F1[((-I) e + p - 2 c s + c v)/d, -\[Beta], (d - I e + p - 2 c s + c v)/d, -((b E^(d z))/a)])/ (((-I) e - p - 2 c s + c v) ((-I) e + p - 2 c s + c v)) + (E^(((-I) e + p + 2 c s - c v) z) ((-I) e - p + 2 c s - c v) Hypergeometric2F1[((-I) e + p + 2 c s - c v)/d, -\[Beta], (d - I e + p + 2 c s - c v)/d, -((b E^(d z))/a)] + E^((I e + p - 2 c s + c v) z) ((-I) e + p + 2 c s - c v) Hypergeometric2F1[(I e + p - 2 c s + c v)/d, -\[Beta], (d + I e + p - 2 c s + c v)/d, -((b E^(d z))/a)])/ (((-I) e - p + 2 c s - c v) ((-I) e + p + 2 c s - c v))), {s, 0, Floor[(1/2) (-1 + v)]}])/(1 + (b E^(d z))/a)^\[Beta] /; Element[v, Integers] && v > 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