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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh and tanh





http://functions.wolfram.com/01.22.21.0156.01









  


  








Input Form





Integrate[(A + B Tanh[z] + C Coth[z])/(a + b Sinh[z]), z] == (2 Cosh[z] (2 a b Sqrt[-a^2 - b^2] B ArcTan[Tanh[z/2]] + 2 a A (a^2 + b^2) ArcTan[(b - a Tanh[z/2])/Sqrt[-a^2 - b^2]] + Sqrt[-a^2 - b^2] (a^2 B Log[Cosh[z]] + (a^2 + b^2) C Log[Sinh[z]] - (b^2 C + a^2 (B + C)) Log[a + b Sinh[z]])) Sinh[z] (A + C Coth[z] + B Tanh[z]))/(a (a - I b) (a + I b) Sqrt[-a^2 - b^2] (-B + C + (B + C) Cosh[2 z] + A Sinh[2 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