Integrate[z^n Cos[b z^2 + e] Cosh[c z^2]^v, z] == (-2^(-2 - v)) z^(1 + n) Binomial[v, v/2] (E^(I e) ((-I) b z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (-I) b z^2] + ((I b z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, I b z^2])/E^(I e)) (1 - Mod[v, 2]) - 2^(-2 - v) z^(1 + n) Sum[Binomial[v, s] (E^(I e) (((-I) b + 2 c s - c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) b + 2 c s - c v) z^2] + (((I b + 2 c s - c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I b + 2 c s - c v) z^2])/E^(I e) + E^(I e) (((-I) b - 2 c s + c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, ((-I) b - 2 c s + c v) z^2] + (((I b - 2 c s + c v) z^2)^((1/2) (-1 - n)) Gamma[(1 + n)/2, (I b - 2 c s + c v) z^2])/E^(I e)), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[n, Integers] && n >= 0 && Element[v, Integers] && v > 0

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