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SinIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinIntegral[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/06.37.21.0064.01









  


  










Input Form





Integrate[z^3 ExpIntegralEi[b z] SinIntegral[a z], z] == (-(I/4)) ((1/b^4) (3 (ExpIntegralEi[((-I) a + b) z] - ExpIntegralEi[(I a + b) z])) - (1/(2 b^3)) ((6 E^(((-I) a + b) z))/((-I) a + b) - (6 E^((I a + b) z))/(I a + b) - (3 b Gamma[2, (-I) a z - b z])/(I a + b)^2 - (3 b Gamma[2, I a z - b z])/ (a + I b)^2 - (b^2 Gamma[3, (-I) a z - b z])/(I a + b)^3 + (b^2 Gamma[3, I a z - b z])/((-I) a + b)^3) - (1/(2 a^4)) ((6 a E^(((-I) a + b) z))/(a + I b) - (6 a E^((I a + b) z))/(a - I b) - 6 ExpIntegralEi[((-I) a + b) z] + 6 ExpIntegralEi[(I a + b) z] + (3 a^2 Gamma[2, (-I) a z - b z])/ (I a + b)^2 + (3 a^2 Gamma[2, I a z - b z])/(a + I b)^2 - (a^3 Gamma[3, (-I) a z - b z])/(a - I b)^3 + (a^3 Gamma[3, I a z - b z])/ (a + I b)^3 - ExpIntegralEi[b z] Gamma[4, (-I) a z] + ExpIntegralEi[b z] Gamma[4, I a z]) + I (z^4 ExpIntegralEi[b z] + Gamma[4, (-b) z]/b^4) SinIntegral[a z])










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