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http://functions.wolfram.com/01.07.21.1367.01
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Integrate[(a - a Cos[c z]^2)^\[Beta] Cos[d z], z] ==
(-(1/(d^2 - 4 c^2 \[Beta]^2)))
((I 2^(-1 - 2 \[Beta]) (((-I) (-1 + E^(2 I c z)))/E^(I c z))^(2 \[Beta])
(E^(2 I d z) (d + 2 c \[Beta]) Hypergeometric2F1[d/(2 c) - \[Beta],
-2 \[Beta], 1 + d/(2 c) - \[Beta], E^(2 I c z)] -
(d - 2 c \[Beta]) Hypergeometric2F1[-((d + 2 c \[Beta])/(2 c)),
-2 \[Beta], 1 - d/(2 c) - \[Beta], E^(2 I c z)])
(a Sin[c z]^2)^\[Beta])/(E^(I d z) (1 - E^(2 I c z))^(2 \[Beta])
Sin[c z]^(2 \[Beta])))
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type='integer'> 2 </cn> </apply> <apply> <power /> <ci> β </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> β </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> <ci> d </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -2 </cn> <ci> β </ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> 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