Cosine: Integration (formula 01.07.21.1313)

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))^nu)^beta cos(d z)

http://functions.wolfram.com/01.07.21.1313.01

Input Form

Integrate[Sqrt[(a + b Cos[c z])^3] Cos[c z], z] == (Sqrt[(a + b Cos[c z])^3] (4 (a^3 + a^2 b + 3 a b^2 + 3 b^3) Sqrt[(a + b Cos[c z])/(a + b)] EllipticE[(c z)/2, (2 b)/(a + b)] - 4 a (a^2 - b^2) Sqrt[(a + b Cos[c z])/(a + b)] EllipticF[(c z)/2, (2 b)/(a + b)] + 2 b (4 a^2 + b^2 + 6 a b Cos[c z] + b^2 Cos[2 c z]) Sin[c z]))/ (10 b c (a + b Cos[c z])^2)

Standard Form

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MathML Form

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<plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> EllipticF </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2002-12-18