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

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

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

 1 + n
x      (-1 + (1 + n) Log[x])
----------------------------
                 2
          (1 + n)
Time to compute: 0.02 second
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