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

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2002-12-18