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Coth






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.22.21.0037.01









  


  










Input Form





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










Standard Form





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MathML Form







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










Rule Form





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





2002-12-18