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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 cosh > Involving (a cosh(z)+b csch(z))-n





http://functions.wolfram.com/01.23.21.0439.01









  


  










Input Form





Integrate[1/(a Cosh[z] + b Csch[z]), z] == (((1 + I)/4) (4 Sqrt[I a + 2 b] ArcTan[((-1 + I) Sqrt[a] + ((1 + I) Sqrt[a] - Sqrt[2 I a + 4 b]) Tanh[z/2])/Sqrt[2 I a - 4 b]] - 4 Sqrt[I a + 2 b] ArcTan[((1 - I) Sqrt[a] - ((1 + I) Sqrt[a] + Sqrt[2 I a + 4 b]) Tanh[z/2])/Sqrt[2 I a - 4 b]] - I Sqrt[4 I a - 8 b] (Log[Sqrt[2 I a + 4 b] + (1 + I) Sqrt[a] Cosh[z] - (1 - I) Sqrt[a] Sinh[z]] - Log[Sqrt[2 I a + 4 b] - (1 + I) Sqrt[a] Cosh[z] + (1 - I) Sqrt[a] Sinh[z]])))/ (Sqrt[a] Sqrt[2 I a - 4 b] Sqrt[I a + 2 b])










Standard Form





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MathML Form







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<ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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