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

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

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

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