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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 Si and power





http://functions.wolfram.com/06.38.21.0069.01









  


  










Input Form





Integrate[z^2 SinIntegral[b z] CosIntegral[a z], z] == (1/6) ((1/b^3) (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] + ExpIntegralEi[(-I) (a + b) z] + ExpIntegralEi[I (a + b) z]) - (1/(2 b^2)) ((1/(a^2 - b^2)) (-8 b Cos[a z] Cos[b z] + b (-a^2 + b^2) z^2 (ExpIntegralE[-1, (-I) (a - b) z] + ExpIntegralE[-1, I (a - b) z] + ExpIntegralE[-1, (-I) (a + b) z] + ExpIntegralE[-1, I (a + b) z]) - 8 a Sin[a z] Sin[b z])) - (1/b^3) (CosIntegral[a z] (Gamma[3, (-I) b z] + Gamma[3, I b z])) + 2 z^3 CosIntegral[a z] SinIntegral[b z] - (1/a^3) (((a^2 - b^2)^2 (ExpIntegralEi[(-I) (a - b) z] + ExpIntegralEi[I (a - b) z] - ExpIntegralEi[(-I) (a + b) z] - ExpIntegralEi[I (a + b) z]) + 2 a b Cos[b z] (2 (-2 a^2 + b^2) Cos[a z] + a (-a^2 + b^2) z Sin[a z]) + 2 a^2 (a (a - b) (a + b) z Cos[a z] + (-3 a^2 + b^2) Sin[a z]) Sin[b z])/(a^2 - b^2)^2 + I (Gamma[3, (-I) a z] - Gamma[3, I a z]) SinIntegral[b z]))










Standard Form





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MathML Form







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





2001-10-29





© 1998-2014 Wolfram Research, Inc.