# How do you integrate int e^(2x)/(1+e^(2x))dx?

Nov 21, 2016

The answer is $= \frac{1}{2} \ln \left(1 + {e}^{2 x}\right) + C$

#### Explanation:

Let's do it by substitution

Let $u = 1 + {e}^{2 x}$

then, $\mathrm{du} = 2 {e}^{2 x} \mathrm{dx}$

$\int \frac{{e}^{2 x} \mathrm{dx}}{1 + {e}^{2 x}}$

$= \frac{1}{2} \int \frac{\mathrm{du}}{u} = \frac{1}{2} \ln \left\mid u \right\mid$

$= \frac{1}{2} \ln \left(1 + {e}^{2 x}\right) + C$