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


Integrate[1/(x^3*Sqrt[a^2 + x^2]), x] ==
-(a*Sqrt[a^2 + x^2] + x^2*Log[a*x] - x^2*Log[-4*a^3*(a + Sqrt[a^2 + x^2])])/(2*a^3*x^2)



                 1
Integrate[----------------, x] == 
           3       2    2
          x  Sqrt[a  + x ]

          2    2     2
-(a Sqrt[a  + x ] + x  Log[a x] - 
 
      2         3            2    2           3  2
     x  Log[-4 a  (a + Sqrt[a  + x ])]) / (2 a  x )

Time to compute: 0.06 second

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