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http://functions.wolfram.com/01.19.21.0634.01
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Integrate[Sin[b z^r + e]^m Sinh[c z^r], z] ==
-((1/r) ((-(1/2))^(1 + m) z Binomial[m, m/2]
((-((-c) z^r)^(-r^(-1))) Gamma[1/r, (-c) z^r] +
Gamma[1/r, c z^r]/(c z^r)^r^(-1)) (1 - Mod[m, 2]))) -
(1/r) ((2^(-1 - m) z Sum[(-1)^k Binomial[m, k]
((E^(-2 I e k + I e m) Gamma[1/r, (-c + 2 I b k - I b m) z^r])/
((-c + 2 I b k - I b m) z^r)^r^(-1) -
(E^(-2 I e k + I e m) Gamma[1/r, (c + 2 I b k - I b m) z^r])/
((c + 2 I b k - I b m) z^r)^r^(-1) + ((-1)^m E^(2 I e k - I e m)
Gamma[1/r, (-c - 2 I b k + I b m) z^r])/
((-c - 2 I b k + I b m) z^r)^r^(-1) +
((-1)^(1 + m) E^(2 I e k - I e m) Gamma[1/r, (c - 2 I b k + I b m)
z^r])/((c - 2 I b k + I b m) z^r)^r^(-1)),
{k, 0, Floor[(1/2) (-1 + m)]}])/I^m) /; Element[m, Integers] && m > 0
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