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-(ExpIntegralE[n, -((1 + m)*Log[x])]*Log[x]^(1 - n))

Integrate[x^m/Log[x]^n, x] ==
-(ExpIntegralE[n, -((1 + m)*Log[x])]*Log[x]^(1 - n)) 

             m
            x
Integrate[-------, x] == 
                n
          Log[x]

                                           1 - n
-(ExpIntegralE[n, -((1 + m) Log[x])] Log[x]     )
Time to compute: 0.08 second
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