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

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2002-12-18