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 Cosh

 http://functions.wolfram.com/01.20.21.1321.01

 Input Form

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