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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving sinh > Involving sinh(b z)





http://functions.wolfram.com/01.22.21.0065.01









  


  










Input Form





Integrate[Sinh[b z] Coth[c z], z] == (1/(2 (4 c^2 b - b^3))) (((-(4 c^2 - b^2)) E^(2 c z) Hypergeometric2F1[-(b/(2 c)), 1, 1 - b/(2 c), E^(2 c z)] - (4 c^2 - b^2) E^(2 (c + b) z) Hypergeometric2F1[b/(2 c), 1, 1 + b/(2 c), E^(2 c z)] + b ((2 c + b) E^(4 c z) Hypergeometric2F1[1 - b/(2 c), 1, 2 - b/(2 c), E^(2 c z)] - (2 c - b) E^(2 (2 c + b) z) Hypergeometric2F1[ 1 + b/(2 c), 1, 2 + b/(2 c), E^(2 c z)]))/E^((2 c + b) z))










Standard Form





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MathML Form







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<cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <ci> b </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18