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-ArcTanh[2*x]

Integrate[(-1 + 2*x)^(-1) - (1 + 2*x)^(-1), x] ==
-ArcTanh[2*x] 

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

-ArcTanh[2 x]
Time to compute: < 0.01 second
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