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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 rational functions of the direct function and hyperbolic functions > Involving rational functions of sinh > Involving (a sinh(c z)+b tanh(c z))-n





http://functions.wolfram.com/01.21.21.0352.01









  


  










Input Form





Integrate[1/(a Sinh[c z] + b Tanh[c z])^2, z] == (Coth[c z] ((-(b + a Cosh[c z])) (-2 a b + (a^2 + b^2) Cosh[c z]) Sech[c z] - (1/Sqrt[a^2 - b^2]) (2 b (2 a^2 + b^2) ArcTan[((-a + b) Tanh[(c z)/2])/Sqrt[a^2 - b^2]] (b + a Cosh[c z]) Tanh[c z]) - a b^2 Sinh[c z] Tanh[c z]))/ ((a^2 - b^2)^2 c (b + a Cosh[c 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