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

$\frac{1}{2} \ln \left(1 + {e}^{2 x}\right) + C$
int e^(2x)/(1+e^(2x) dx
Integrate by substitution. Let $u = 1 + {e}^{2 x}$. Thsi makes $\mathrm{du} = 2 {e}^{2 x}$
$\int {e}^{2 x} / \left(1 + {e}^{2 x}\right) \mathrm{dx} = \frac{1}{2} \int \frac{1}{u} \mathrm{du} = \frac{1}{2} \ln \left\mid u \right\mid + C$
$= \frac{1}{2} \ln \left(1 + {e}^{2 x}\right) + C$