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


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

Time to compute: < 0.01 second

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