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Integrate[x^(3/2)*Sqrt[2*a*x - x^2], x] ==
(2*Sqrt[-(x*(-2*a + x))]*(-64*a^3 - 16*a^2*x - 6*a*x^2 + 15*x^3))/(105*Sqrt[x])

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

(2 Sqrt[-(x (-2 a + x))] 
 
          3       2          2       3
    (-64 a  - 16 a  x - 6 a x  + 15 x )) / 
 
  (105 Sqrt[x])