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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving algebraic functions of sinh > Involving (a+b sinh(d z))beta cosh(c z)





http://functions.wolfram.com/01.20.21.1648.01









  


  








Input Form





Integrate[Cosh[2 a z]/(Sqrt[Sinh[a z]] (1 + Sinh[a z])), z] == (1/a) (2 (-1)^(1/4) Sqrt[Cosh[a z]^2] (-2 I EllipticE[I ArcSinh[(-1)^(1/4) Sqrt[Sinh[a z]]], -1] + (2 + 2 I) EllipticF[I ArcSinh[(-1)^(1/4) Sqrt[Sinh[a z]]], -1] - 3 EllipticPi[-I, I ArcSinh[(-1)^(1/4) Sqrt[Sinh[a z]]], -1]) Sech[a 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