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





http://functions.wolfram.com/01.07.21.1324.01









  


  










Input Form





Integrate[Sqrt[a + b Cos[c z]]/(d + e Cos[c z])^2, z] == ((4 a d - b e) Sqrt[(a + b Cos[c z])/(a + b)] EllipticPi[(2 e)/(d + e), (c z)/2, (2 b)/(a + b)])/(2 c (d - e) (d + e)^2 Sqrt[a + b Cos[c z]]) + (1/(b c (d^2 - e^2))) (I Sqrt[-(1/(a + b))] (a^2 - b^2) Sqrt[(b (1 + Cos[c z]))/(-a + b)] Sqrt[(b - b Cos[c z])/(a + b)] Csc[c z] EllipticE[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Cos[c z]]], (a + b)/(a - b)]) + (I Sqrt[(-b - b Cos[c z])/(a - b)] Sqrt[(b - b Cos[c z])/(a + b)] Csc[c z] EllipticF[I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Cos[c z]]], (a + b)/(a - b)])/(Sqrt[-(1/(a + b))] c e (d + e)) + (I b (2 d^2 + e^2) Sqrt[(b (1 + Cos[c z]))/(-a + b)] Sqrt[(b - b Cos[c z])/(a + b)] Csc[c z] EllipticPi[((a + b) e)/((-b) d + a e), I ArcSinh[Sqrt[-(1/(a + b))] Sqrt[a + b Cos[c z]]], (a + b)/(a - b)])/ (2 Sqrt[-(1/(a + b))] c e (b d - a e) (-d^2 + e^2)) - (e Sqrt[a + b Cos[c z]] Sin[c z])/(c (d - e) (d + e) (d + e Cos[c z]))










Standard Form





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MathML Form







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<mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mi> c </mi> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> e </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msup> <mi> e </mi> <mn> 2 </mn> </msup> <mo> - </mo> <msup> <mi> d </mi> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> 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Rule Form





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





2002-12-18