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-PolyLog[2, 1 - x]

Integrate[Log[x]/(-1 + x), x] ==
-PolyLog[2, 1 - x] 

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

-PolyLog[2, 1 - x]
Time to compute: 0.01 second
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