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-(1 + 2*Log[x]*(1 + Log[x]))/(4*x^2)

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

                2
          Log[x]
Integrate[-------, x] == 
             3
            x

-(1 + 2 Log[x] (1 + Log[x]))
----------------------------
               2
            4 x
Time to compute: < 0.01 second
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