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 Cosh

 http://functions.wolfram.com/01.20.21.1320.01

 Input Form

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

 Standard Form

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

 2002-12-18