Integrate[z^2 SinhIntegral[b z] CoshIntegral[a z], z] == (1/12) ((1/b^3) (2 (ExpIntegralEi[(a - b) z] + ExpIntegralEi[(-a + b) z] + ExpIntegralEi[(-(a + b)) z] + ExpIntegralEi[(a + b) z])) - (1/b^3) (2 CoshIntegral[a z] (Gamma[3, (-b) z] + Gamma[3, b z])) - (-8 b Cosh[a z] Cosh[b z] + (a - b) b (a + b) z^2 (ExpIntegralE[-1, (a - b) z] + ExpIntegralE[-1, (-a + b) z] + ExpIntegralE[-1, (-(a + b)) z] + ExpIntegralE[-1, (a + b) z]) + 8 a Sinh[a z] Sinh[b z])/((a - b) b^2 (a + b)) + 4 z^3 CoshIntegral[a z] SinhIntegral[b z] - (1/a^3) (2 (ExpIntegralEi[(a - b) z] + ExpIntegralEi[(-a + b) z] - ExpIntegralEi[(-(a + b)) z] - ExpIntegralEi[(a + b) z] + (1/(a^2 - b^2)^2) (2 a (Cosh[b z] (2 b (-2 a^2 + b^2) Cosh[a z] + a (a - b) b (a + b) z Sinh[a z]) - a (a (a - b) (a + b) z Cosh[a z] + (-3 a^2 + b^2) Sinh[a z]) Sinh[b z])) + Gamma[3, (-a) z] SinhIntegral[b z] - Gamma[3, a z] SinhIntegral[b z])))

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2001-10-29