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http://functions.wolfram.com/01.07.21.0498.01
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Integrate[Cos[a ArcSec[z]], z] == (1/(2 (-1 + a^2)))
((-2 a (1 + a) E^(I ArcSec[z]) Hypergeometric2F1[1/2 - a/2, 1, 3/2 - a/2,
-E^(2 I ArcSec[z])] + (-1 + a) ((1 + a) (1 + E^(2 I a ArcSec[z])) z -
2 a E^(I (1 + 2 a) ArcSec[z]) Hypergeometric2F1[(1 + a)/2, 1,
(3 + a)/2, -E^(2 I ArcSec[z])]))/E^(I a ArcSec[z]))
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