Cosine: Integration (formula 01.07.21.1382)

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))^nu)^beta

http://functions.wolfram.com/01.07.21.1382.01

Input Form

Integrate[Sqrt[(a + b Cos[c z]^2)^5], z] == (Sqrt[(2 a + b + b Cos[2 c z])^5] (32 (23 a^3 + 46 a^2 b + 31 a b^2 + 8 b^3) Sqrt[(2 a + b + b Cos[2 c z])/(a + b)] EllipticE[c z, b/(a + b)] - 128 a (2 a^2 + 3 a b + b^2) Sqrt[(2 a + b + b Cos[2 c z])/(a + b)] EllipticF[c z, b/(a + b)] + 2 Sqrt[2] b (88 a^2 + 88 a b + 25 b^2 + 28 b (2 a + b) Cos[2 c z] + 3 b^2 Cos[4 c z]) Sin[2 c z]))/ (480 c (2 a + b + b Cos[2 c z])^3)

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