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

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2002-12-18