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(x*Sqrt[a^2 - x^2]*(-a^2 + 2*x^2) + a^4*ArcTan[x/Sqrt[a^2 - x^2]])/8

Integrate[x^2*Sqrt[a^2 - x^2], x] ==
(x*Sqrt[a^2 - x^2]*(-a^2 + 2*x^2) + a^4*ArcTan[x/Sqrt[a^2 - x^2]])/8 

           2       2    2
Integrate[x  Sqrt[a  - x ], x] == 

         2    2     2      2
(x Sqrt[a  - x ] (-a  + 2 x ) + 
 
     4              x
    a  ArcTan[-------------]) / 8
                    2    2
              Sqrt[a  - x ]
Time to compute: 0.08 second
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