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 Cosh

 http://functions.wolfram.com/01.20.21.3885.01

 Input Form

 Integrate[(E^(p z) Sin[d z] Cosh[e z])/(a + b Cosh[c z])^2, z] == (-(1/4)) I (-((E^((c - I d - e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - I d - e + p)/c, 1, 2 + ((-I) d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - I d - e + p)/c, 1, 2 + ((-I) d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + (-a^2 + b^2) (Hypergeometric2F1[(c - I d - e + p)/c, 2, 2 + ((-I) d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] - Hypergeometric2F1[ (c - I d - e + p)/c, 2, 2 + ((-I) d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2] (Hypergeometric2F1[(c - I d - e + p)/c, 2, 2 + ((-I) d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[ (c - I d - e + p)/c, 2, 2 + ((-I) d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/(b (a^2 - b^2)^(3/2) (c - I d - e + p))) + (E^((c + I d - e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + I d - e + p)/c, 1, 2 + (I d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + I d - e + p)/c, 1, 2 + (I d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + (-a^2 + b^2) (Hypergeometric2F1[(c + I d - e + p)/c, 2, 2 + (I d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] - Hypergeometric2F1[(c + I d - e + p)/c, 2, 2 + (I d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2] (Hypergeometric2F1[(c + I d - e + p)/c, 2, 2 + (I d - e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[ (c + I d - e + p)/c, 2, 2 + (I d - e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/ (b (a^2 - b^2)^(3/2) (c + I d - e + p)) - (E^((c - I d + e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ (c - I d + e + p)/c, 1, 2 + ((-I) d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c - I d + e + p)/c, 1, 2 + ((-I) d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + (-a^2 + b^2) (Hypergeometric2F1[(c - I d + e + p)/c, 2, 2 + ((-I) d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] - Hypergeometric2F1[(c - I d + e + p)/c, 2, 2 + ((-I) d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2] (Hypergeometric2F1[(c - I d + e + p)/c, 2, 2 + ((-I) d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[ (c - I d + e + p)/c, 2, 2 + ((-I) d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/ (b (a^2 - b^2)^(3/2) (c - I d + e + p)) + (E^((c + I d + e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[ (c + I d + e + p)/c, 1, 2 + (I d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + I d + e + p)/c, 1, 2 + (I d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + (-a^2 + b^2) (Hypergeometric2F1[(c + I d + e + p)/c, 2, 2 + (I d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] - Hypergeometric2F1[(c + I d + e + p)/c, 2, 2 + (I d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2] (Hypergeometric2F1[(c + I d + e + p)/c, 2, 2 + (I d + e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[ (c + I d + e + p)/c, 2, 2 + (I d + e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/ (b (a^2 - b^2)^(3/2) (c + I d + e + p)))

 Standard Form

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

 2002-12-18