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6*x^(1/6) - 3*x^(1/3) + 2*Sqrt[x] - 6*Log[1 + x^(1/6)]

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

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

   1/6      1/3                          1/6
6 x    - 3 x    + 2 Sqrt[x] - 6 Log[1 + x   ]
Time to compute: 0.01 second
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