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

Integrate[1/(-(b/E^(m*x)) + a*E^(m*x)), x] ==
-(ArcTanh[(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
  ArcTanh[------------]
            Sqrt[b]
-(---------------------)
    Sqrt[a] Sqrt[b] m
Time to compute: 0.02 second
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