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x/b - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)

Integrate[x^2/(a + b*x^2), x] ==
x/b - (Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2) 

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

                   Sqrt[b] x
    Sqrt[a] ArcTan[---------]
x                   Sqrt[a]
- - -------------------------
b              3/2
              b
Time to compute: 0.02 second
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