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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/01.22.21.0253.01









  


  










Input Form





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










Standard Form





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MathML Form







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





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