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Integrate[x^3*Sqrt[a^2 - x^2], x] ==
-(((a - x)*(a + x))^(3/2)*(2*a^2 + 3*x^2))/15

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

                   3/2     2      2
-(((a - x) (a + x))    (2 a  + 3 x ))
-------------------------------------
                 15