Cosine: Integration (formula 01.07.21.1358)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving functions of the direct function

Involving algebraic functions of the direct function

Involving (a+b cos²(c z))^beta

http://functions.wolfram.com/01.07.21.1358.01

Input Form

Integrate[(a + b Cos[c z]^2)^\[Beta], z] == (-(1/(b c (1 + \[Beta])))) (2^(-1 - \[Beta]) AppellF1[1 + \[Beta], 1/2, 1/2, 2 + \[Beta], (2 a + b + b Cos[2 c z])/(2 a), (2 a + b + b Cos[2 c z])/(2 (a + b))] Sqrt[-((b Cos[c z]^2)/a)] (2 a + b + b Cos[2 c z])^(1 + \[Beta]) Csc[2 c z] Sqrt[(b Sin[c z]^2)/(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