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((a^3 - 3*a*x^2)/(x^2*Sqrt[-a^2 + x^2]) + 3*ArcTan[a/Sqrt[-a^2 + x^2]])/(2*a^5)

Integrate[1/(x^3*(-a^2 + x^2)^(3/2)), x] ==
((a^3 - 3*a*x^2)/(x^2*Sqrt[-a^2 + x^2]) + 3*ArcTan[a/Sqrt[-a^2 + x^2]])/(2*a^5) 

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

    3        2
   a  - 3 a x                      a
----------------- + 3 ArcTan[--------------]
 2        2    2                    2    2
x  Sqrt[-a  + x ]            Sqrt[-a  + x ]
--------------------------------------------
                       5
                    2 a
Time to compute: 0.13 second
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