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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 sinn(c z)(a+b cos(2c z))beta





http://functions.wolfram.com/01.07.21.2306.01









  


  










Input Form





Integrate[Sin[c z]^4 (a + b Cos[2 c z])^(3/2), z] == (-8 (a^4 + 8 a^3 b - 30 a^2 b^2 - 16 a b^3 + 21 b^4) Sqrt[(a + b Cos[2 c z])/(a + b)] EllipticE[c z, (2 b)/(a + b)] + 8 (a^4 + 7 a^3 b - 11 a^2 b^2 - 7 a b^3 + 10 b^4) Sqrt[(a + b Cos[2 c z])/(a + b)] EllipticF[c z, (2 b)/(a + b)] + b (4 a^3 - 112 a^2 b + 106 a b^2 - 28 b^3 + b (36 a^2 - 168 a b + 95 b^2) Cos[2 c z] + 2 (13 a - 14 b) b^2 Cos[4 c z] + 5 b^3 Cos[6 c z]) Sin[2 c z])/(560 b^2 c Sqrt[a + b Cos[2 c z]])










Standard Form





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MathML Form







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</mo> <mrow> <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> <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'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -8 </cn> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <cos /> 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</ci> <cn type='integer'> 2 </cn> </apply> <ci> c </ci> <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> </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