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CosIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > CosIntegral[z] > Integration > Indefinite integration > Involving direct function and Gamma-, Beta-, Erf-type functions > Involving exponential integral-type functions and a power function > Involving Ei and power





http://functions.wolfram.com/06.38.21.0064.01









  


  










Input Form





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










Standard Form





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MathML Form







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</apply> <apply> <ci> CosIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2001-10-29





© 1998- Wolfram Research, Inc.