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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: 0.05 second
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