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 Cosh

 http://functions.wolfram.com/01.20.21.0870.01

 Input Form

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

 Standard Form

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

 2002-12-18