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

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

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

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