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(3*Log[1 + x^(2/3)])/2


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



             1
Integrate[--------, x] == 
           1/3
          x    + x

           2/3
3 Log[1 + x   ]
---------------
       2

Time to compute: < 0.01 second

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