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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[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/06.35.21.0033.01









  


  










Input Form





Integrate[z^n Cos[b z] ExpIntegralEi[a z], z] == ((1/(2 b)) I ((-ExpIntegralEi[(a - I b) z]) n! + ExpIntegralEi[a z] Gamma[1 + n, I b z] + n! Sum[(b^k Gamma[k, (-a + I b) z])/((I a + b)^k k!), {k, 1, n}] + (-1)^n (ExpIntegralEi[(a + I b) z] n! - ExpIntegralEi[a z] Gamma[1 + n, (-I) b z] - n! Sum[(b^k Gamma[k, (-(a + I b)) z])/ (((-I) a + b)^k k!), {k, 1, n}])))/(I b)^n /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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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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