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

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

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

       x
----------------
              2
c Sqrt[c + a x ]
Time to compute: 0.02 second
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