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 Cos

 http://functions.wolfram.com/01.07.21.2649.01

 Input Form

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

 Standard Form

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 MathML Form

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

 2002-12-18