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(Sqrt[1 - x^4] + x^2*ArcSin[x^2])/2


Integrate[x*ArcSin[x^2], x] ==
(Sqrt[1 - x^4] + x^2*ArcSin[x^2])/2



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

          4     2         2
Sqrt[1 - x ] + x  ArcSin[x ]
----------------------------
             2

Time to compute: 0.02 second

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