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 Cosh

 http://functions.wolfram.com/01.20.21.4872.01

 Input Form

 Integrate[(E^(p z) Sin[e z] Sinh[d z])/(a + b Cosh[c z]), z] == (1/4) I (-((E^((c - d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - d - I e + p)/c, 1, 2 + (-d - I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - d - I e + p)/c, 1, 2 + (-d - I e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/(b Sqrt[a^2 - b^2] (c - d - I e + p))) + (E^((c + d - I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d - I e + p)/c, 1, 2 + (d - I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d - I e + p)/c, 1, 2 + (d - I e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + d - I e + p)) + (E^((c - d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ (c - d + I e + p)/c, 1, 2 + (-d + I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - d + I e + p)/c, 1, 2 + (-d + I e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/(b Sqrt[a^2 - b^2] (c - d + I e + p)) - (E^((c + d + I e + p) z) ((a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d + I e + p)/c, 1, 2 + (d + I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d + I e + p)/c, 1, 2 + (d + I e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]))/ (b Sqrt[a^2 - b^2] (c + d + I e + p)))

 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