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

                 1
Integrate[---------------, x] == 
               2    2 3/2
          x (-a  + x )

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