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

                  1
Integrate[-----------------, x] == 
           3        2    2
          x  Sqrt[-a  + x ]

                              a
                 ArcTan[--------------]
       2    2                  2    2
Sqrt[-a  + x ]          Sqrt[-a  + x ]
-------------- - ----------------------
      2  2                   3
   2 a  x                 2 a