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

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

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

                        Sqrt[b] x
                 ArcTan[---------]
      x                  Sqrt[a]
-------------- + -----------------
            2        3/2
2 a (a + b x )    2 a    Sqrt[b]
Time to compute: 0.06 second
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