Cosine: Integration (formula 01.07.21.2340)

Cos

$Mathematica Notation$

Elementary Functions

Cos[z]

Integration

Indefinite integration

Involving functions of the direct function and trigonometric functions

Involving algebraic functions of the direct function and trigonometric functions

Involving sin

Involving sin^m(c z)cos^m(c z)(a+b cos(2c z))^beta

http://functions.wolfram.com/01.07.21.2340.01

Input Form

Integrate[(Sin[c z]^4 Cos[c z]^2)/Sqrt[a + b Cos[2 c z]], z] == (4 (4 a^3 + 9 a^2 b + 2 a b^2 - 3 b^3) Sqrt[(a + b Cos[2 c z])/(a + b)] EllipticE[c z, (2 b)/(a + b)] - 4 (4 a^3 + 5 a^2 b - 4 a b^2 - 5 b^3) Sqrt[(a + b Cos[2 c z])/(a + b)] EllipticF[c z, (2 b)/(a + b)] + b (-8 a^2 - 10 a b + 3 b^2 - 2 b (a + 5 b) Cos[2 c z] + 3 b^2 Cos[4 c z]) Sin[2 c z])/(240 b^3 c Sqrt[a + b Cos[2 c z]])

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