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(3*x^2 - 6*x^2*Log[x] + 6*x^2*Log[x]^2 + 4*Log[x]^3)/12

Integrate[((1 + x^2)*Log[x]^2)/x, x] ==
(3*x^2 - 6*x^2*Log[x] + 6*x^2*Log[x]^2 + 4*Log[x]^3)/ 12 

                2        2
          (1 + x ) Log[x]
Integrate[----------------, x] == 
                 x

   2      2             2       2           3
3 x  - 6 x  Log[x] + 6 x  Log[x]  + 4 Log[x]
---------------------------------------------
                     12
Time to compute: < 0.01 second
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