Integrate[z^n E^(p z) Cos[b z] Sinh[c z^2], z] == (2^(-4 - n) (-c)^(-n - 1) (E^((p (2 I b + 3 p))/(4 c)) Sum[(I b - p)^(n - q) ((-I) b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, ((-I) b + p - 2 c z)^2/(4 c)], {q, 0, n}] + 2^n E^((3 p (2 I b + p))/(4 c)) Sum[(((-I) b - p)^(n - q) (I b + p - 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (I b + p - 2 c z)^2/(4 c)])/2^n, {q, 0, n}] + (-1)^n E^((2 b^2 + 2 I b p + p^2)/(4 c)) (2^n Sum[(((-I) b - p)^(n - q) (I b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, -((I b + p + 2 c z)^2/(4 c))])/2^n, {q, 0, n}] + E^((I b p)/c) Sum[(I b - p)^(n - q) ((-I) b + p + 2 c z)^(1 + q) Binomial[n, q] ExpIntegralE[(1 - q)/2, (b + I (p + 2 c z))^2/(4 c)], {q, 0, n}])))/ E^((b^2 + 4 I b p + 2 p^2)/(4 c)) /; Element[n, Integers] && n >= 0

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2002-12-18