Sine integral: Integration (formula 06.37.21.0062)

SinIntegral

$Mathematica Notation$

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/06.37.21.0062.01

Input Form

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