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

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

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

            2             2
x Sqrt[1 - x ] + (-1 + 2 x ) ArcSin[x]
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                  4
Time to compute: 0.03 second
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