Evaluate the indefinite integral $\int\frac{dx}{(1+e^x)^2}$ > Evaluate the indefinite integral $$\int\frac{dx}{(1+e^x)^2}$$ There is some clever trick to solve this, I think. I'm really hesitant to ask a homework question without submitting an attempted solution, but this question is not very conducive towards partial solutions.

You are given $$I = \int {\frac{{dx}}{{{{\left( {{e^x} + 1} \right)}^2}}}} $$

Let $e^x+1=u$. Then, what does you integral become?

**SPOILER** You should get

> $I = \displaystyle \int {\frac{{du}}{{{u^2}\left( {u - 1} \right)}}}$

Then use partial fraction decomposition.