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-ArcTan[3/Sqrt[-9 + 4*x^2]]/3

Integrate[1/(x*Sqrt[-9 + 4*x^2]), x] ==
-ArcTan[3/Sqrt[-9 + 4*x^2]]/3 

                  1
Integrate[-----------------, x] == 
                         2
          x Sqrt[-9 + 4 x ]

               3
-ArcTan[---------------]
                     2
        Sqrt[-9 + 4 x ]
------------------------
           3
Time to compute: 0.01 second
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