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(-x + 2*Log[-4*(3 + E^(2*x))])/3

Integrate[(-1 + E^(2*x))/(3 + E^(2*x)), x] ==
(-x + 2*Log[-4*(3 + E^(2*x))])/3 

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

                    2 x
-x + 2 Log[-4 (3 + E   )]
-------------------------
            3
Time to compute: < 0.01 second
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