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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving (a+b coth(c z))-n





http://functions.wolfram.com/01.22.21.0252.01









  


  










Input Form





Integrate[(A + B Coth[z])/(a + b Coth[z])^3, z] == ((A + B Coth[z]) Csch[z]^2 (b Cosh[z] + a Sinh[z]) ((b^2 (A b - a B))/((a - b)^2 (a + b)^2) - (2 (-3 a A b + 2 a^2 B + b^2 B) Sinh[z] (b Cosh[z] + a Sinh[z]))/ ((a - b)^2 (a + b)^2) + (2 (a^3 A + 3 a A b^2 - 3 a^2 b B - b^3 B) z (b Cosh[z] + a Sinh[z])^2)/((a - b)^3 (a + b)^3) + (1/(a^2 - b^2)^3) (2 (-3 a^2 A b - A b^3 + a^3 B + 3 a b^2 B) Log[b Cosh[z] + a Sinh[z]] (b Cosh[z] + a Sinh[z])^2)))/ (2 (a + b Coth[z])^3 (B Cosh[z] + A Sinh[z]))










Standard Form





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MathML Form







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<apply> <times /> <ci> A </ci> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> B </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3 </cn> <ci> A </ci> <ci> b </ci> <ci> a </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> B </ci> </apply> </apply> <apply> <sinh /> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <ci> b </ci> <apply> <coth /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <apply> <times /> <ci> B </ci> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> A </ci> <apply> <sinh /> <ci> z </ci> </apply> </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





© 1998- Wolfram Research, Inc.