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

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

                     2
Integrate[ArcSin[a x] , x] == 

                   2  2
       2 Sqrt[1 - a  x ] ArcSin[a x]                2
-2 x + ----------------------------- + x ArcSin[a x]
                     a
Time to compute: 0.03 second
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