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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 csch2(z)+b sech2(z))-n





http://functions.wolfram.com/01.24.21.0462.01









  


  










Input Form





Integrate[1/(a Csch[z]^2 + b Sech[z]^2)^2, z] == ((a - b + (a + b) Cosh[2 z]) Csch[z]^4 Sech[z]^4 (24 a^3 z - 168 a^2 b z + 168 a b^2 z - 24 b^3 z + 96 a^(5/2) Sqrt[b] ArcTan[(Sqrt[b] Tanh[z])/Sqrt[a]] - 192 a^(3/2) b^(3/2) ArcTan[(Sqrt[b] Tanh[z])/Sqrt[a]] + 96 Sqrt[a] b^(5/2) ArcTan[(Sqrt[b] Tanh[z])/Sqrt[a]] + 24 (a + b) ((a^2 - 6 a b + b^2) z + 4 Sqrt[a] (a - b) Sqrt[b] ArcTan[(Sqrt[b] Tanh[z])/Sqrt[a]]) Cosh[2 z] - 3 (5 a^3 - 17 a^2 b - 17 a b^2 + 5 b^3) Sinh[2 z] - 6 a^3 Sinh[4 z] - 6 a^2 b Sinh[4 z] + 6 a b^2 Sinh[4 z] + 6 b^3 Sinh[4 z] + a^3 Sinh[6 z] + 3 a^2 b Sinh[6 z] + 3 a b^2 Sinh[6 z] + b^3 Sinh[6 z]))/ (256 (a + b)^4 (a Csch[z]^2 + b Sech[z]^2)^2)










Standard Form





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MathML Form







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</ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 24 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 6 </cn> <ci> b </ci> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <ci> b </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <arctan /> <apply> <times 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Rule Form





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





2002-12-18





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