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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 rational functions of sinh > Involving f(z)(a+b cosh(c z))beta





http://functions.wolfram.com/01.20.21.4386.01









  


  










Input Form





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










Standard Form





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MathML Form







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<times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> <ci> b </ci> </apply> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <sech /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18