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RootSum[1 + 5*#1 + #1^5 & , Log[x - #1]/(1 + #1^4) & ]/5


Integrate[1/(1 + 5*x + x^5), x] ==
RootSum[1 + 5*#1 + #1^5 & , Log[x - #1]/(1 + #1^4) & ]/5



               1
Integrate[------------, x] == 
                     5
          1 + 5 x + x

                     5     Log[x - #1]
RootSum[1 + 5 #1 + #1  & , ----------- & ]
                                   4
                             1 + #1
------------------------------------------
                    5

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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