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Integrate[1/(x^2*Sqrt[(a^2 - x^2)^3]), x] ==
(-a^4 + 3*a^2*x^2 - 2*x^4)/(a^4*x*Sqrt[(a^2 - x^2)^3])

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

  4      2  2      4
-a  + 3 a  x  - 2 x
---------------------
 4          2    2 3
a  x Sqrt[(a  - x ) ]