Cosine: Integration (formula 01.07.21.0740)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving trigonometric functions

Involving rational functions of sin

Involving cos(c z)/a+b sin²(d z)

http://functions.wolfram.com/01.07.21.0740.01

Input Form

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

Standard Form

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MathML Form

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Rule Form

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

2002-12-18