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(x*Sqrt[1 - x^2]*(15 + 10*x^2 + 8*x^4) + 3*(-5 + 16*x^6)*ArcSin[x])/288

Integrate[x^5*ArcSin[x], x] ==
(x*Sqrt[1 - x^2]*(15 + 10*x^2 + 8*x^4) + 3*(-5 + 16*x^6)*ArcSin[x])/288 

           5
Integrate[x  ArcSin[x], x] == 

             2            2      4
(x Sqrt[1 - x ] (15 + 10 x  + 8 x ) + 
 
                6
    3 (-5 + 16 x ) ArcSin[x]) / 288
Time to compute: 0.05 second
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