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(x*(Sqrt[1 - 1/(a^2*x^2)] + a*x*ArcCsc[a*x]))/(2*a)

Integrate[x*ArcCsc[a*x], x] ==
(x*(Sqrt[1 - 1/(a^2*x^2)] + a*x*ArcCsc[a*x]))/(2*a) 

Integrate[x ArcCsc[a x], x] == 

              1
x (Sqrt[1 - -----] + a x ArcCsc[a x])
             2  2
            a  x
-------------------------------------
                 2 a
Time to compute: 0.05 second
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