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(x*Sqrt[a^2 + x^2]*(a^2 + 2*x^2) - a^4*Log[2*(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*Log[2*(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                  2    2
    a  Log[2 (x + Sqrt[a  + x ])]) / 8
Time to compute: 0.05 second
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