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Sqrt[a^2 + x^2] + a*Log[a^3*x] - a*Log[2*a*(a + Sqrt[a^2 + x^2])]

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

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

      2    2           3
Sqrt[a  + x ] + a Log[a  x] - 
 
                       2    2
  a Log[2 a (a + Sqrt[a  + x ])]
Time to compute: 0.03 second
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