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Cot






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.09.21.0068.01









  


  










Input Form





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










Standard Form





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MathML Form







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</cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </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> <imaginaryi /> <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