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Tanh




Mathematica Notation

Traditional Notation









Elementary Functions > Tanh[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving sinh > Involving sinh(c z)(a+b tanh2(c z))beta





http://functions.wolfram.com/01.21.21.0358.01









  


  








Input Form





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








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