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

Jul 5, 2015

$\arctan {e}^{x} + c$.

#### Explanation:

First of all, I think there is a little mistake in your writing, maybe it would be:

$\int {e}^{x} / \left(1 + {e}^{2 x}\right) \mathrm{dx} = \left(1\right)$.

This is a easy integral if you rimember this rule:

$\int \frac{f ' \left(x\right)}{1 + {\left[f \left(x\right)\right]}^{2}} \mathrm{dx} = \arctan f \left(x\right) + c$,

so our integral is:

$\left(1\right) = \arctan {e}^{x} + c$.