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(2*ArcTan[x^(3/2)/Sqrt[a^3 - x^3]])/3

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

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

              3/2
             x
2 ArcTan[-------------]
               3    3
         Sqrt[a  - x ]
-----------------------
           3
Time to compute: 0.05 second
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