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CosIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CosIntegral[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions and a power function > Involving cos and power





http://functions.wolfram.com/06.38.21.0032.01









  


  










Input Form





Integrate[z^2 Cos[b z] CosIntegral[a z], z] == (1/(2 b^3)) (I (-ExpIntegralEi[(-I) (a - b) z] + CosIntegral[a z] (Gamma[3, (-I) b z] - Gamma[3, I b z]) + ((a^2 - b^2)^2 (ExpIntegralEi[I (a - b) z] + ExpIntegralEi[ (-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + 2 I b Cos[b z] ((a - b) b^2 (a + b) z Cos[a z] + 2 a (a^2 - 2 b^2) Sin[a z]) + 2 I b^2 ((-(a^2 - 3 b^2)) Cos[a z] + a (a - b) (a + b) z Sin[a z]) Sin[b z])/((a - b)^2 (a + b)^2)))










Standard Form





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MathML Form







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/> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <cos /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> ExpIntegralEi </ci> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a 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Rule Form





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





2001-10-29





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