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

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2002-12-18