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Cos






Mathematica Notation

Traditional 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 sinm(c z)cosm(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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<mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </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> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </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> <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> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 9 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> </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> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 5 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 5 </cn> <apply> 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Rule Form





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





2002-12-18