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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1eb zr+ecos(c zr)





http://functions.wolfram.com/01.07.21.0399.01









  


  










Input Form





Integrate[(1/z^5) E^(b Sqrt[z] + e) Cos[c Sqrt[z]], z] == (1/(40320 z^4)) (E^e ((-E^((b - I c) Sqrt[z])) (5040 + (b - I c) Sqrt[z] (720 + 120 (b - I c) Sqrt[z] + 24 (b - I c)^2 z + 6 (b - I c)^3 z^(3/2) + 2 (b - I c)^4 z^2 + (b - I c)^5 z^(5/2) + (b - I c)^6 z^3)) - E^((b + I c) Sqrt[z]) (5040 + (b + I c) Sqrt[z] (720 + 120 (b + I c) Sqrt[z] + 24 (b + I c)^2 z + 6 (b + I c)^3 z^(3/2) + 2 (b + I c)^4 z^2 + (b + I c)^5 z^(5/2) + (b + I c)^6 z^3)))) + ((b - I c)^8 E^e ExpIntegralEi[(b - I c) Sqrt[z]])/40320 + ((b + I c)^8 E^e ExpIntegralEi[(b + I c) Sqrt[z]])/40320










Standard Form





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MathML Form







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<cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 120 </cn> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 720 </cn> </apply> </apply> <cn type='integer'> 5040 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <exponentiale /> <ci> e </ci> </apply> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 40320 </cn> <cn type='integer'> -1 </cn> </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