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

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Answer 1 · 2015-07-05T15:55:43

$arctane^x+c$ .

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:

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

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