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-(x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), x^n])

Integrate[1/(-1 + x^n), x] ==
-(x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), x^n]) 

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

                         1      1   n
-(x Hypergeometric2F1[1, -, 1 + -, x ])
                         n      n
Time to compute: < 0.01 second
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