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ArcSin[(3*Log[x])/2]/3

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

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

       3 Log[x]
ArcSin[--------]
          2
----------------
       3
Time to compute: 0.01 second
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