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

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2002-12-18