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(x*Sqrt[a^2 + x^2])/2 - (a^2*Log[2*(x + Sqrt[a^2 + x^2])])/2

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

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

        2    2     2                  2    2
x Sqrt[a  + x ]   a  Log[2 (x + Sqrt[a  + x ])]
--------------- - -----------------------------
       2                        2
Time to compute: 0.03 second
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