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 Cosh

 http://functions.wolfram.com/01.20.21.4228.01

 Input Form

 Integrate[Sinh[d z]/(a + b Cosh[c z])^2, z] == (1/(2 b (a^2 - b^2)^(3/2))) ((1/(c + d)) (E^((c + d) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d)/c, 1, 2 + d/c, (b E^(c z))/ (-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d)/c, 1, 2 + d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] - a^2 Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + b^2 Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] - a Sqrt[a^2 - b^2] Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, (b E^(c z))/ (-a + Sqrt[a^2 - b^2])] + a^2 Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] - b^2 Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] - a Sqrt[a^2 - b^2] Hypergeometric2F1[(c + d)/c, 2, 2 + d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])) + (1/(c - d)) (E^((c - d) z) ((-a) (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[1 - d/c, 1, 2 - d/c, (b E^(c z))/ (-a + Sqrt[a^2 - b^2])] + a (a - Sqrt[a^2 - b^2]) Hypergeometric2F1[1 - d/c, 1, 2 - d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + a^2 Hypergeometric2F1[1 - d/c, 2, 2 - d/c, (b E^(c z))/ (-a + Sqrt[a^2 - b^2])] - b^2 Hypergeometric2F1[1 - d/c, 2, 2 - d/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a Sqrt[a^2 - b^2] Hypergeometric2F1[1 - d/c, 2, 2 - d/c, (b E^(c z))/ (-a + Sqrt[a^2 - b^2])] - a^2 Hypergeometric2F1[1 - d/c, 2, 2 - d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + b^2 Hypergeometric2F1[1 - d/c, 2, 2 - d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + a Sqrt[a^2 - b^2] Hypergeometric2F1[1 - d/c, 2, 2 - d/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))

 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