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

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Answer 1 · 2015-04-03T14:23:51

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

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

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

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

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

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