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Integrate[1/(x^2*(a + b*x^2)), x] ==
-(1/(a*x)) - (Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/ a^(3/2)

                1
Integrate[-------------, x] == 
           2         2
          x  (a + b x )

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