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-(a*Sqrt[a^2 - x^2] + x^2*Log[a*x] - x^2*Log[-4*a*(a + Sqrt[a^2 - x^2])])/(2*a*x^2)

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

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

          2    2     2
-(a Sqrt[a  - x ] + x  Log[a x] - 
 
      2                     2    2             2
     x  Log[-4 a (a + Sqrt[a  - x ])]) / (2 a x )
Time to compute: 0.06 second
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