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

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