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x - (2*ArcTan[Sqrt[E]*x])/Sqrt[E]

Integrate[Tanh[1/2 + Log[x]], x] ==
x - (2*ArcTan[Sqrt[E]*x])/Sqrt[E] 

               1
Integrate[Tanh[- + Log[x]], x] == 
               2

    2 ArcTan[Sqrt[E] x]
x - -------------------
          Sqrt[E]
Time to compute: 0.03 second
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