Cosine: Integration (formula 01.07.21.1380)

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))^betacos(d z)

http://functions.wolfram.com/01.07.21.1380.01

Input Form

Integrate[(a + b Cos[c z]^2)^\[Beta] Cos[2 c z], z] == -(2^(-1 - \[Beta]) Sqrt[-((b Cos[c z]^2)/a)] (2 a + b + b Cos[2 c z])^ (1 + \[Beta]) ((-(2 a + b)) (2 + \[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))] + (1 + \[Beta]) AppellF1[2 + \[Beta], 1/2, 1/2, 3 + \[Beta], (2 a + b + b Cos[2 c z])/(2 a), (2 a + b + b Cos[2 c z])/(2 (a + b))] (2 a + b + b Cos[2 c z])) Csc[2 c z] Sqrt[(b Sin[c z]^2)/(a + b)])/ (b^2 c (1 + \[Beta]) (2 + \[Beta]))

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