Integrate[z^n Cos[b z] SinhIntegral[a z], z] == (1/4) (I b)^(-1 - n) n! (ExpIntegralEi[(a - I b) z] - ExpIntegralEi[(-(a + I b)) z] - ExpIntegralEi[(a + I b) z]/(-1)^n + (-1)^n ExpIntegralEi[(-a) z + I b z] + (1/Gamma[2 + n]) (2 (1 + n) ((-1)^n Gamma[1 + n, (-I) b z] - Gamma[1 + n, I b z]) SinhIntegral[a z]) + (-1)^n E^((a + I b) z) Sum[(((I b)/(a + I b))^m Sum[((-a - I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] - (-1)^n E^((-a) z + I b z) Sum[(((I b)/(I b - a))^m Sum[((a - I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] - E^((a - I b) z) Sum[(((I b)/(I b - a))^m Sum[((-a + I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}] + Sum[(((I b)/(I b + a))^m Sum[((a + I b)^k z^k)/k!, {k, 0, -1 + m}])/m, {m, 1, n}]/E^((a + I b) z)) /; Element[n, Integers] && n >= 0

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2001-10-29