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


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



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

              2  2             2  2
a x Sqrt[1 - a  x ] + (-1 + 2 a  x ) ArcSin[a x]
------------------------------------------------
                         2
                      4 a

Time to compute: 0.04 second

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