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What is the integral of #(e^(2x))/(1+e^(2x))#?

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Apr 3, 2015

#1/2 ln (1+e^(2x))+C#

#int e^(2x)/(1+e^(2x) dx#

Integrate by substitution. Let #u=1+e^(2x)#. Thsi makes #du = 2e^(2x)#

#int e^(2x)/(1+e^(2x)) dx = 1/2 int 1/u du = 1/2 ln abs u +C#

#= 1/2 ln (1+e^(2x)) +C#

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