Integrate[Cos[b z] Sinh[c z^2]^v, z] == (Binomial[v, v/2] (1 - Mod[v, 2]) Sin[b z])/((2 I)^v b) + I^v 2^(-(1/2) - v) Sqrt[Pi] Sum[(-1)^s Binomial[v, s] ((1/Sqrt[2 I c s - I c v]) (Cos[(Pi v)/2 + b^2/(4 (2 I c s - I c v))] FresnelC[(-b + 2 (2 I c s - I c v) z)/(Sqrt[2 Pi] Sqrt[2 I c s - I c v])] + FresnelS[(-b + 2 (2 I c s - I c v) z)/ (Sqrt[2 Pi] Sqrt[2 I c s - I c v])] Sin[(Pi v)/2 + b^2/(4 (2 I c s - I c v))]) + (1/Sqrt[-2 I c s + I c v]) (Cos[-((Pi v)/2) + b^2/(4 (-2 I c s + I c v))] FresnelC[(-b + 2 (-2 I c s + I c v) z)/(Sqrt[2 Pi] Sqrt[-2 I c s + I c v])] + FresnelS[(-b + 2 (-2 I c s + I c v) z)/(Sqrt[2 Pi] Sqrt[-2 I c s + I c v])] Sin[-((Pi v)/2) + b^2/(4 (-2 I c s + I c v))])), {s, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

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