Integrate[z^n Sin[b z] Erf[a z], z] == (1/(b^(2 n) (2 b Sqrt[Pi]))) Exp[-(b^2/(4 a^2))] ((-E^(b^2/(4 a^2))) Sqrt[Pi] Erf[a z] (I b)^n (Gamma[1 + n, (-I) b z] + (-1)^n Gamma[1 + n, I b z]) - a ((-I) b)^n n! Sum[((I b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-(((-I) b)/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z - (I b)/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}] - a (I b)^n n! Sum[(((-I) b)^m/m!) (-a^2)^((1/2) (-1 - m)) Sum[Binomial[m, k] (-((I b)/(2 Sqrt[-a^2])))^(m - k) (Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^(1 + k) (-(Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^2)^((1/2) (-1 - k)) Gamma[(1 + k)/2, -(Sqrt[-a^2] z + (I b)/(2 Sqrt[-a^2]))^2], {k, 0, m}], {m, 0, n}]) /; Element[n, Integers] && n >= 0

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