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(x*Sqrt[-a^2 + x^2])/2 - (a^2*Log[2*(x + Sqrt[-a^2 + x^2])])/2


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



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

         2    2     2                   2    2
x Sqrt[-a  + x ]   a  Log[2 (x + Sqrt[-a  + x ])]
---------------- - ------------------------------
       2                         2

Time to compute: 0.03 second

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