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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving inverse trigonometric functions > Involving tan-1





http://functions.wolfram.com/01.07.21.0492.01









  


  










Input Form





Integrate[Cos[a ArcTan[z]], z] == (1/(2 (-4 + a^2))) ((I a (2 + a) E^(2 I ArcTan[z]) Hypergeometric2F1[1 - a/2, 1, 2 - a/2, -E^(2 I ArcTan[z])] + (-2 + a) (I a E^(2 I (1 + a) ArcTan[z]) Hypergeometric2F1[1 + a/2, 1, 2 + a/2, -E^(2 I ArcTan[z])] + (2 + a) (z + E^(2 I a ArcTan[z]) z - I Hypergeometric2F1[-(a/2), 1, 1 - a/2, -E^(2 I ArcTan[z])] - I E^(2 I a ArcTan[z]) Hypergeometric2F1[a/2, 1, 1 + a/2, -E^(2 I ArcTan[z])])))/ E^(I a ArcTan[z]))










Standard Form





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MathML Form







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2 </cn> <imaginaryi /> <apply> <arctan /> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <arctan /> <ci> z </ci> </apply> </apply> </apply> <imaginaryi /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <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 /> <ci> a </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <apply> <arctan /> <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