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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 sinh2(e z)+b cosh2(e z))beta





http://functions.wolfram.com/01.20.21.4417.01









  


  










Input Form





Integrate[1/Sqrt[a Sinh[e z]^2 + b Cosh[e z]^2], z] == -2 I (1 + Cosh[e z]) Sqrt[(-a + b + (a + b) Cosh[2 e z])/(1 + Cosh[e z])^2] EllipticF[I ArcSinh[Sqrt[(2 a + b - 2 Sqrt[a] Sqrt[a + b])/b] Tanh[(e z)/2]], (2 a + b + 2 Sqrt[a] Sqrt[a + b])/ (2 a + b - 2 Sqrt[a] Sqrt[a + b])] Sqrt[1 + (b Tanh[(e z)/2]^2)/(2 a + b - 2 Sqrt[a] Sqrt[a + b])] (Sqrt[1 + (b Tanh[(e z)/2]^2)/(2 a + b + 2 Sqrt[a] Sqrt[a + b])]/ (Sqrt[(2 a + b - 2 Sqrt[a] Sqrt[a + b])/b] e Sqrt[-a + b + (a + b) Cosh[2 e z]] Sqrt[4 a Tanh[(e z)/2]^2 + b (1 + Tanh[(e z)/2]^2)^2]))










Standard Form





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MathML Form







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</cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <tanh /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </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