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 Cosh

 http://functions.wolfram.com/01.20.21.0864.01

 Input Form

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

 Standard Form

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

 2002-12-18