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Sech




Mathematica Notation

Traditional Notation









Elementary Functions > Sech[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 csch > Involving (a csch(z)+b sech(z))-n





http://functions.wolfram.com/01.24.21.0460.01









  


  








Input Form





Integrate[1/(a Csch[z] + b Sech[z])^2, z] == (Csch[z] Sech[z]^2 (a Cosh[z] + b Sinh[z]) (-(1/a) + Csch[z] (a Cosh[z] + b Sinh[z]) (-((4 (a^4 + 6 a^2 b^2 + b^4) z)/((a - b)^3 (a + b)^3)) - (4 a b Cosh[2 z])/((a - b)^2 (a + b)^2) + (16 a b (a^2 + b^2) Log[a Cosh[z] + b Sinh[z]])/(a^2 - b^2)^3 + ((a^4 + 6 a^2 b^2 + b^4) Sinh[z])/(a (a - b)^2 (a + b)^2 (a Cosh[z] + b Sinh[z])) + (2 (a^2 + b^2) Sinh[2 z])/ ((a - b)^2 (a + b)^2))))/(8 (a Csch[z] + b Sech[z])^2)








Standard Form





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MathML Form







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</annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18