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-x + Log[1 - E^(a*x)]/a

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

              1
Integrate[---------, x] == 
                a x
          -1 + E

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