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ArcTan[(Sqrt[a]*E^(m*x))/Sqrt[b]]/(Sqrt[a]*Sqrt[b]*m)

Integrate[1/(b/E^(m*x) + a*E^(m*x)), x] ==
ArcTan[(Sqrt[a]*E^(m*x))/Sqrt[b]]/(Sqrt[a]*Sqrt[b]*m) 

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

                m x
       Sqrt[a] E
ArcTan[------------]
         Sqrt[b]
--------------------
 Sqrt[a] Sqrt[b] m
Time to compute: 0.02 second
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