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(Log[-1 - x] - Log[-1 + x])/2

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

            1
Integrate[------, x] == 
               2
          1 - x

Log[-1 - x] - Log[-1 + x]
-------------------------
            2
Time to compute: < 0.01 second
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