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

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

                                          3/2
          x           3    3             x
2 Sqrt[-------] Sqrt[a  - x ] ArcTan[-------------]
        3    3                             3    3
       a  - x                        Sqrt[a  - x ]
---------------------------------------------------
                     3 Sqrt[x]