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

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

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