Cosine: Integration (formula 01.07.21.1332)

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 cos(c z))^betaand rational function of cos(c z)

http://functions.wolfram.com/01.07.21.1332.01

Input Form

Integrate[Cos[c z]/((d + e Cos[c z]) Sqrt[a + b Cos[c z]]), z] == -(2 I Sqrt[(b (1 + Cos[c z]))/(-a + b)] Sqrt[(b - b Cos[c z])/(a + b)] Csc[c z] (((-b) d + a e) EllipticF[ I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Cos[c z]]], (a + b)/(a - b)] + b d EllipticPi[((a + b) e)/((-b) d + a e), I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Cos[c z]]], (a + b)/(a - b)]))/ (b Sqrt[-(1/(a + b))] c e (b d - a e))

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