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 Cosh

 http://functions.wolfram.com/01.20.21.4879.01

 Input Form

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