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

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2002-12-18