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http://functions.wolfram.com/01.19.21.3228.01
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Integrate[E^(p z) Cos[d + c z]^m Sinh[b + a z]^\[Nu], z] ==
(Sinh[b + a z]^\[Nu] (-((1/(p - a \[Nu])) (E^(p z) Binomial[m, m/2]
Hypergeometric2F1[(p - a \[Nu])/(2 a), -\[Nu],
(1/2) (2 + p/a - \[Nu]), E^(2 (b + a z))] (-1 + Mod[m, 2]))) +
Sum[E^((-I) d m + 2 I d s) Binomial[m, s]
((E^(2 I d (m - 2 s) + (p + I c (m - 2 s)) z) Hypergeometric2F1[
(I c m + p - 2 I c s - a \[Nu])/(2 a), -\[Nu],
(1/2) (2 + (I c m + p - 2 I c s)/a - \[Nu]), E^(2 (b + a z))])/
(I c m + p - 2 I c s - a \[Nu]) + (E^(((-I) c m + p + 2 I c s) z)
Hypergeometric2F1[((-I) c m + p + 2 I c s - a \[Nu])/(2 a), -\[Nu],
(2 a - I c m + p + 2 I c s - a \[Nu])/(2 a), E^(2 (b + a z))])/
((-I) c m + p + 2 I c s - a \[Nu])),
{s, 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}
