Question

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

Answer 1

`arctane^x+c`.

Explanation:

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

`inte^x/(1+e^(2x))dx=(1)`.

This is a easy integral if you rimember this rule:

`int(f'(x))/(1+[f(x)]^2)dx=arctanf(x)+c`,

so our integral is:

`(1)=arctane^x+c`.