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-(Sqrt[(a^2 - x^2)^3]*(x*Sqrt[a^2 - x^2]*(-5*a^2 + 2*x^2) - 3*a^4*ArcTan[x/Sqrt[a^2 - x^2]]))/(8*(a^2 - x^2)^(3/2))

Integrate[Sqrt[(a^2 - x^2)^3], x] ==
-(Sqrt[(a^2 - x^2)^3]*(x*Sqrt[a^2 - x^2]* (-5*a^2 + 2*x^2) - 3*a^4*ArcTan[x/Sqrt[a^2 - x^2]]))/ (8*(a^2 - x^2)^(3/2)) 

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

         2    2 3           2    2       2      2
-(Sqrt[(a  - x ) ] (x Sqrt[a  - x ] (-5 a  + 2 x ) - 
 
          4              x                 2    2 3/2
       3 a  ArcTan[-------------])) / (8 (a  - x )   )
                         2    2
                   Sqrt[a  - x ]
Time to compute: 0.16 second
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