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Log[-3 - E^(2*x)]/2

Integrate[E^(2*x)/(3 + E^(2*x)), x] ==
Log[-3 - E^(2*x)]/2 

             2 x
            E
Integrate[--------, x] == 
               2 x
          3 + E

          2 x
Log[-3 - E   ]
--------------
      2
Time to compute: < 0.01 second
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