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Cos






Mathematica Notation

Traditional 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 cosnu(c z)





http://functions.wolfram.com/01.07.21.1396.01









  


  










Input Form





Integrate[(a + b Cos[c z]^2)^(3/2) Cos[c z]^4, z] == (-128 (a^4 - a^3 b - 14 a^2 b^2 - 20 a b^3 - 8 b^4) Sqrt[(2 a + b + b Cos[2 c z])/(a + b)] EllipticE[c z, b/(a + b)] + 64 a (2 a^3 - 3 a^2 b - 13 a b^2 - 8 b^3) Sqrt[(2 a + b + b Cos[2 c z])/(a + b)] EllipticF[c z, b/(a + b)] + Sqrt[2] b (32 a^3 + 496 a^2 b + 684 a b^2 + 250 b^3 + b (144 a^2 + 480 a b + 299 b^2) Cos[2 c z] + 2 b^2 (26 a + 27 b) Cos[4 c z] + 5 b^3 Cos[6 c z]) Sin[2 c z])/ (2240 b^2 c Sqrt[2 a + b + b Cos[2 c z]])










Standard Form





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MathML Form







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</cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> c </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <ci> b </ci> <apply> <times /> <ci> b </ci> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18