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

1 Answer
Jul 5, 2015

Answer:

#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#.