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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b cosh2(c z))betaand rational function of cosh(c z)





http://functions.wolfram.com/01.20.21.2425.01









  


  










Input Form





Integrate[1/((d + e Cosh[c z]) Sqrt[a + b Cosh[c z]^2]), z] == (Sqrt[(2 a + b + b Cosh[2 c z])/a] (d ArcTan[(Sqrt[2 + (2 b d^2)/(a e^2)] Sinh[c z])/(Sqrt[1 - d^2/e^2] Sqrt[(2 a + b + b Cosh[2 c z])/a])] + I Sqrt[1 - d^2/e^2] Sqrt[1 + (b d^2)/(a e^2)] e EllipticPi[e^2/d^2, Pi/2 - I 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 Cosh[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