Integrate[z^(\[Alpha] - 1) Sinh[b z^r + e]^m Cosh[c z^r + g], z] == 2^(-1 - m) z^\[Alpha] ((1/r) ((Binomial[m, m/2] ((E^g Gamma[\[Alpha]/r, (-c) z^r])/ ((-c) z^r)^(\[Alpha]/r) + Gamma[\[Alpha]/r, c z^r]/ (E^g (c z^r)^(\[Alpha]/r))) (-1 + Mod[m, 2]))/I^m) - (1/r) Sum[(-1)^k E^(-g + 2 e k - e m) Binomial[m, k] ((E^(2 g - 4 e k + 2 e m) Gamma[\[Alpha]/r, (-c + 2 b k - b m) z^r])/ ((-c + 2 b k - b m) z^r)^(\[Alpha]/r) + (E^(-4 e k + 2 e m) Gamma[\[Alpha]/r, (c + 2 b k - b m) z^r])/ ((c + 2 b k - b m) z^r)^(\[Alpha]/r) + ((-1)^m E^(2 g) Gamma[\[Alpha]/r, (-c - 2 b k + b m) z^r])/ ((-c - 2 b k + b m) z^r)^(\[Alpha]/r) + ((-1)^m Gamma[\[Alpha]/r, (c - 2 b k + b m) z^r])/ ((c - 2 b k + b m) z^r)^(\[Alpha]/r)), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0

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