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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric, exponential and a power functions > Involving sin, exp and power > Involving zalpha-1 eb zr+e sin(a zr+q) cos(c zr+g)





http://functions.wolfram.com/01.07.21.0995.01









  


  








Input Form





Integrate[z^n E^(b Sqrt[z] + e) Sin[a Sqrt[z] + q] Cos[c Sqrt[z] + g], z] == (I/2) ((E^(e + I g + I q) Gamma[2 (1 + n), ((-I) a - b - I c) Sqrt[z]])/ ((-I) a - b - I c)^(2 (1 + n)) - (E^(e + I g - I q) Gamma[2 (1 + n), (I a - b - I c) Sqrt[z]])/ (I a - b - I c)^(2 (1 + n)) + (E^(e - I g + I q) Gamma[2 (1 + n), ((-I) a - b + I c) Sqrt[z]])/ ((-I) a - b + I c)^(2 (1 + n)) - (E^(e - I g - I q) Gamma[2 (1 + n), (I a - b + I c) Sqrt[z]])/ (I a - b + I c)^(2 (1 + n))) /; Element[n, Integers] && n >= 0








Standard Form





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MathML Form







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<apply> <plus /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> c </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> n </ci> <ci> &#8469; </ci> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18