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Csch




Mathematica Notation

Traditional Notation









Elementary Functions > Csch[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 tanh(z)+b csch(z))-n





http://functions.wolfram.com/01.23.21.0442.01









  


  








Input Form





Integrate[1/(a Tanh[z] + b Csch[z])^2, z] == (1/a^2) (((-Sqrt[2]) Sqrt[(-b) (b + Sqrt[4 a^2 + b^2])] (-4 a^4 + b^3 (-b + Sqrt[4 a^2 + b^2]) + a^2 b (-7 b + 5 Sqrt[4 a^2 + b^2])) ArcTan[((2 a - b + Sqrt[4 a^2 + b^2]) Tanh[z/2])/ (Sqrt[2] Sqrt[b] Sqrt[-b + Sqrt[4 a^2 + b^2]])] + Sqrt[b] Sqrt[-b + Sqrt[4 a^2 + b^2]] ((4 a^2 + b^2)^(3/2) Sqrt[(-b) (b + Sqrt[4 a^2 + b^2])] z + Sqrt[2] (4 a^4 + b^3 (b + Sqrt[4 a^2 + b^2]) + a^2 b (7 b + 5 Sqrt[4 a^2 + b^2])) ArcTan[((-2 a + b + Sqrt[4 a^2 + b^2]) Tanh[z/2])/ (Sqrt[2] Sqrt[(-b) (b + Sqrt[4 a^2 + b^2])])]))/ (Sqrt[b] (4 a^2 + b^2)^(3/2) Sqrt[-b + Sqrt[4 a^2 + b^2]] Sqrt[(-b) (b + Sqrt[4 a^2 + b^2])]) - (a ((-a) b + (2 a^2 + b^2) Cosh[z]) Sinh[z])/ ((4 a^2 + b^2) (b Cosh[z] + a Sinh[z]^2)))








Standard Form





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MathML Form







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type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18