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http://functions.wolfram.com/01.19.21.2532.01
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Integrate[Sin[d + c z]^m Sinh[b + a z]^\[Nu], z] ==
((1/(a \[Nu])) Sinh[b + a z]^\[Nu]
((-Binomial[m, m/2]) Hypergeometric2F1[-(\[Nu]/2), -\[Nu], 1 - \[Nu]/2,
E^(-2 (b + a z))] (-1 + Mod[m, 2]) + I^(1 - m) a \[Nu]
Sum[(-1)^k E^(I d (-2 k + m)) Binomial[m, k]
((E^(I c (-2 k + m) z) Hypergeometric2F1[
(I (2 c k - c m + I a \[Nu]))/(2 a), -\[Nu],
(1/2) (2 - (I c (-2 k + m))/a - \[Nu]), E^(-2 (b + a z))])/
(2 c k - c m + I a \[Nu]) -
(E^(I (4 d k - 2 d m + m Pi + 2 c k z - c m z)) Hypergeometric2F1[
(I (c (-2 k + m) + I a \[Nu]))/(2 a), -\[Nu],
(1/2) (2 - (I c (2 k - m))/a - \[Nu]), E^(-2 (b + a z))])/
(2 c k - c m - I a \[Nu])), {k, 0, Floor[(1/2) (-1 + m)]}]))/
(2^m (1 - E^(-2 (b + a z)))^\[Nu]) /; Element[m, Integers] && m > 0
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){kind=small}
