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

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