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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/01.22.21.0410.01









  


  










Input Form





Integrate[Tanh[c z] (a + b Coth[c z]^2)^\[Beta], z] == (1/(2 c)) ((a + b Coth[c z]^2)^\[Beta] ((1/((a + b) (1 + \[Beta]))) ((a + b Coth[c z]^2) Hypergeometric2F1[1 + \[Beta], 1, 2 + \[Beta], (a + b Coth[c z]^2)/ (a + b)]) + (1/\[Beta]) (Hypergeometric2F1[-\[Beta], -\[Beta], 1 - \[Beta], -((a Tanh[c z]^2)/b)]/(1 + (a Tanh[c z]^2)/b)^\[Beta])))










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