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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function and hyperbolic functions > Involving algebraic functions of the direct function and hyperbolic functions > Involving tanh > Involving tanh(c z)(a+b coth2(c z))beta





http://functions.wolfram.com/01.22.21.0411.01









  


  








Input Form





Integrate[Tanh[c z] Sqrt[a + b Coth[c z]^2], z] == ((-Sqrt[a]) Sqrt[a + b] ArcSinh[(Sqrt[a] Tanh[c z])/Sqrt[b]] (b Coth[c z] + a Tanh[c z]) + Sqrt[b] (a + b) ArcTanh[Sqrt[a + b Coth[c z]^2]/Sqrt[a + b]] Sqrt[a + b Coth[c z]^2] Sqrt[1 + (a Tanh[c z]^2)/b])/(Sqrt[b] Sqrt[a + b] c Sqrt[a + b Coth[c z]^2] Sqrt[1 + (a Tanh[c z]^2)/b])








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