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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+b tanh(d z)+c coth(d z))-n





http://functions.wolfram.com/01.22.21.0391.01









  


  








Input Form





Integrate[1/(a + b Tanh[d z] + c Coth[d z]), z] == (Csch[d z] (2 a (b - c) ArcTan[(a + 2 b Tanh[d z])/Sqrt[-a^2 + 4 b c]] + Sqrt[-a^2 + 4 b c] (2 a d z - (b + c) Log[-b + c + (b + c) Cosh[2 d z] + a Sinh[2 d z]])) Sech[d z] (-b + c + (b + c) Cosh[2 d z] + a Sinh[2 d z]))/(4 (a - b - c) (a + b + c) Sqrt[-a^2 + 4 b c] d (a + c Coth[d z] + b Tanh[d 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