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


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



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

                                        1 - n
-(Gamma[1 - n, -((1 + m) Log[x])] Log[x]      
 
                       -1 + n
    (-((1 + m) Log[x]))      )

Time to compute: 0.06 second

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