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

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2001-10-29