Integrate[E^(p z) Sin[c z]^m Cosh[b + a z], z] == (1/(a^2 - p^2)) ((E^(p z)/2^m) Binomial[m, m/2] (-1 + Mod[m, 2]) (p Cosh[b + a z] - a Sinh[b + a z])) + 2^(1 - m) Sum[(-1)^k E^(p z) Binomial[m, k] ((Cos[(m Pi)/2] (c (2 k - m) Sin[c (-2 k + m) z] ((-a^2 - c^2 (-2 k + m)^2 - p^2) Cosh[b + a z] + 2 a p Sinh[b + a z]) - Cos[c (-2 k + m) z] (p (a^2 - c^2 (-2 k + m)^2 - p^2) Cosh[b + a z] + a (-a^2 - c^2 (-2 k + m)^2 + p^2) Sinh[b + a z])) - Sin[(m Pi)/2] (c (2 k - m) Cos[c (-2 k + m) z] ((-a^2 - c^2 (-2 k + m)^2 - p^2) Cosh[b + a z] + 2 a p Sinh[b + a z]) + Sin[c (-2 k + m) z] (p (a^2 - c^2 (-2 k + m)^2 - p^2) Cosh[b + a z] + a (-a^2 - c^2 (-2 k + m)^2 + p^2) Sinh[b + a z])))/ (a^4 + 2 a^2 (c^2 (-2 k + m)^2 - p^2) + (c^2 (-2 k + m)^2 + p^2)^2)), {k, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0

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2002-12-18