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http://functions.wolfram.com/03.05.21.0020.01
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Integrate[Sinh[(2/3) (a z)^(3/2)] AiryAi[a z], z] ==
(z (-6 Gamma[4/3] HypergeometricPFQ[{1/6, 2/3}, {1/3, 5/3},
(-(4/3)) (a z)^(3/2)] + 6 Gamma[4/3] HypergeometricPFQ[{1/6, 2/3},
{1/3, 5/3}, (4/3) (a z)^(3/2)] + 3^(1/3) a z Gamma[2/3]
(HypergeometricPFQ[{5/6, 4/3}, {5/3, 7/3}, (-(4/3)) (a z)^(3/2)] -
HypergeometricPFQ[{5/6, 4/3}, {5/3, 7/3}, (4/3) (a z)^(3/2)])))/
(12 3^(2/3) Gamma[2/3] Gamma[4/3])
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<ci> AiryAi </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 12 </cn> <apply> <power /> <cn type='integer'> 3 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 2 <sep /> 3 </cn> </apply> <apply> <ci> Gamma </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> z </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 6 </cn> <apply> <ci> Gamma </ci> <cn type='rational'> 4 <sep /> 3 </cn> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <cn type='rational'> 1 <sep /> 6 </cn> <cn type='rational'> 2 <sep /> 3 </cn> </list> <list> <cn type='rational'> 1 <sep /> 3 </cn> <cn type='rational'> 5 <sep /> 3 </cn> </list> <apply> <times /> <cn type='rational'> 4 <sep /> 3 </cn> <apply> <power /> <apply> 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Date Added to functions.wolfram.com (modification date)
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