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x*Log[1 + x^(-1)] + Log[1 + x]

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

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

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