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 Cosh

 http://functions.wolfram.com/01.20.21.1241.01

 Input Form

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

 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