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(x*Sqrt[-a^2 + x^2]*(3*a^4 - 14*a^2*x^2 + 8*x^4) + 3*a^6*Log[2*(x + Sqrt[-a^2 + x^2])])/48

Integrate[x^2*(-a^2 + x^2)^(3/2), x] ==
(x*Sqrt[-a^2 + x^2]*(3*a^4 - 14*a^2*x^2 + 8*x^4) + 3*a^6*Log[2*(x + Sqrt[-a^2 + x^2])])/48 

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

          2    2      4       2  2      4
(x Sqrt[-a  + x ] (3 a  - 14 a  x  + 8 x ) + 
 
       6                   2    2
    3 a  Log[2 (x + Sqrt[-a  + x ])]) / 48
Time to compute: 0.09 second
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