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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 rational functions of the direct function and hyperbolic functions > Involving rational functions of tanh > Involving (a tanh2(c z)+b coth2(c z))-n





http://functions.wolfram.com/01.22.21.0393.01









  


  








Input Form





Integrate[1/(a Tanh[c z]^2 + b Coth[c z]^2), z] == (2 a^(1/4) b^(1/4) c z + (-1)^(1/4) (Sqrt[a] + I Sqrt[b]) ArcTan[((-1)^(1/4) a^(1/4) Tanh[c z])/b^(1/4)] + (-1)^(1/4) (I Sqrt[a] + Sqrt[b]) ArcTan[((-1)^(3/4) a^(1/4) Tanh[c z])/ b^(1/4)])/(2 a^(1/4) b^(1/4) (a + b) c)








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