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RootSum[1 + #1^2 + #1^3 & , (x - Log[-E^x + #1])/(3 + #1^2) & ]


Integrate[1/(1 + E^(2*x) + E^(3*x)), x] ==
RootSum[1 + #1^2 + #1^3 & , (x - Log[-E^x + #1])/(3 + #1^2) & ]



                 1
Integrate[---------------, x] == 
               2 x    3 x
          1 + E    + E

                                    x
              2     3     x - Log[-E  + #1]
RootSum[1 + #1  + #1  & , ----------------- & ]
                                     2
                               3 + #1

Time to compute: 0.02 second

Log[x]: Log[x]: natural logarithm [properties] RootSum[f, form]: sum over the roots of a polynomial


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