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

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

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

                                  1 + n
-(ExpIntegralE[-n, -Log[x]] Log[x]     )
Time to compute: 0.02 second
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