Integrate[E^(b Sqrt[z] + d z) Sin[c Sqrt[z]]^v, z] == (Binomial[v, v/2] (E^(b Sqrt[z] + d z)/d - (b Sqrt[Pi] Erfi[(b + 2 d Sqrt[z])/(2 Sqrt[d])])/ (E^(b^2/(4 d)) (2 d^(3/2)))) (1 - Mod[v, 2]))/2^v + (1/(I^v d^(3/2))) 2^(-1 - v) Sum[((-1)^k Binomial[v, k] (2 Sqrt[d] E^((b^2 - c^2 (4 k^2 + v^2) + 2 b (I c (2 k + v) + 2 d Sqrt[z]) + 4 I c d (-2 k + v) Sqrt[z] + 4 d^2 z)/(4 d)) + 2 Sqrt[d] E^((b^2 - c^2 (4 k^2 + v^2) + 2 b (I c (2 k + v) + 2 d Sqrt[z]) + 4 I c d (2 k - v) Sqrt[z] + 4 d (I Pi v + d z))/ (4 d)) - E^(((I b c - c^2 k + I d Pi) v)/d) Sqrt[Pi] (b + 2 I c k - I c v) Erfi[(b + 2 I c k - I c v + 2 d Sqrt[z])/ (2 Sqrt[d])] - E^((I c k (2 b + I c v))/d) Sqrt[Pi] (b + I c (-2 k + v)) Erfi[(b + I c (-2 k + v) + 2 d Sqrt[z])/ (2 Sqrt[d])]))/E^((b^2 + 2 I b c (2 k + v) - c^2 (4 k^2 + v^2))/ (4 d)), {k, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

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2002-12-18