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 Cosh

 http://functions.wolfram.com/01.20.21.0686.01

 Input Form

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

 Standard Form

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 MathML Form

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

 2002-12-18