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(x^3*(-1 + 3*Log[x]))/9

Integrate[x^2*Log[x], x] ==
(x^3*(-1 + 3*Log[x]))/9 

           2
Integrate[x  Log[x], x] == 

 3
x  (-1 + 3 Log[x])
------------------
        9
Time to compute: < 0.01 second
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