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 Cosh

 http://functions.wolfram.com/01.20.21.3875.01

 Input Form

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