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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 sin2(c z))betaand rational function of sin(c z)





http://functions.wolfram.com/01.07.21.1415.01









  


  










Input Form





Integrate[1/((d + e Cos[c z]) Sqrt[a + b Cos[c z]^2]), z] == (Sqrt[(2 a + b + b Cos[2 c z])/a] (d ArcTanh[(Sqrt[2 + (2 b d^2)/(a e^2)] Sin[c z])/(Sqrt[1 - d^2/e^2] Sqrt[(2 a + b + b Cos[2 c z])/a])] - Sqrt[1 - d^2/e^2] Sqrt[1 + (b d^2)/(a e^2)] e EllipticPi[e^2/d^2, Pi/2 - c z, -(b/a)]))/ (c d Sqrt[1 - d^2/e^2] Sqrt[1 + (b d^2)/(a e^2)] e Sqrt[2 a + b + b Cos[2 c z]])










Standard Form





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MathML Form







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Rule Form





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





2002-12-18