Integrate[Sinh[b + (2/3) (a z)^(3/2)] AiryBiPrime[a z], z] == (E^(-b - (2/3) (a z)^(3/2)) (-6 (1 + E^(2 b + (4/3) (a z)^(3/2))) (a z)^(3/2) (a^(3/2) z^(3/2))^(2/3) AiryBi[a z] Gamma[5/3] + 15 a (-1 + E^(2 b + (4/3) (a z)^(3/2))) z (a^(3/2) z^(3/2))^(2/3) AiryBiPrime[a z] Gamma[5/3] - Sqrt[3] (3 a^3 (-1 + E^(2 b + (4/3) (a z)^(3/2))) z^3 BesselI[-(4/3), (2/3) a^(3/2) z^(3/2)] Gamma[5/3] + (a^(3/2) z^(3/2))^(1/3) (2 3^(1/3) E^((2/3) (a z)^(3/2)) (-1 + E^(2 b)) (a^(3/2) z^(3/2))^(1/3) + 3 a^(5/2) (-1 + E^(2 b + (4/3) (a z)^(3/2))) z^(5/2) BesselI[4/3, (2/3) a^(3/2) z^(3/2)] Gamma[5/3]))))/ (30 a (a^(3/2) z^(3/2))^(2/3) Gamma[5/3])

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2001-10-29