Cosine: Integration (formula 01.07.21.1414)

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 cos^nu(c z)

http://functions.wolfram.com/01.07.21.1414.01

Input Form

Integrate[Cos[c z]^4/(a + b Cos[c z]^2)^(5/2), z] == (((2 a + b + b Cos[2 c z])/(a + b))^(3/2) (-2 (a + 2 b) EllipticE[c z, b/(a + b)] + (2 a + 3 b) EllipticF[c z, b/(a + b)]) + (1/(a + b)^2) (Sqrt[2] b (a^2 + 4 a b + 2 b^2 + b (a + 2 b) Cos[2 c z]) Sin[2 c z]))/(3 b^2 c (2 a + b + b Cos[2 c z])^(3/2))

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