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Cosh




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.20.21.4395.01









  


  








Input Form





Integrate[1/Sqrt[(a Sinh[e z] + b Cosh[e z])^5], z] == (2 Sech[e z + ArcTanh[b/a]] (b Cosh[e z] + a Sinh[e z]) (Sqrt[Cosh[e z + ArcTanh[b/a]]^2] HypergeometricPFQ[{1/4, 1/2}, {5/4}, -Sinh[e z + ArcTanh[b/a]]^2] (b Cosh[e z] + a Sinh[e z])^2 + (a Cosh[e z] + b Sinh[e z])^2))/(3 a (-a + b) (a + b) Sqrt[1 - b^2/a^2] e Sqrt[(b Cosh[e z] + a Sinh[e z])^5])








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