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

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

                 1
Integrate[---------------, x] == 
           2   2    2 3/2
          x  (a  + x )

       2      2
      a  + 2 x
-(------------------)
   4         2    2
  a  x Sqrt[a  + x ]
Time to compute: 0.03 second
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