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

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

              2
             x
Integrate[---------, x] == 
                2 2
          (8 + x )

                        x
             ArcTan[---------]
    -x              2 Sqrt[2]
---------- + -----------------
        2        4 Sqrt[2]
2 (8 + x )
Time to compute: 0.22 second
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