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


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



Integrate[x ArcCos[x], x] == 

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

Time to compute: 0.03 second

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