Computing $\int \frac{\ln(x)}{(1+x)^2}dx$ I am trying to solve the following integral
$$\int \frac{\ln(x)}{(1+x)^2}dx.$$
I have found a few similar questions on stackexchange but usually involving boundaries, so the answers have involved methods that don't seem applicable when the integral is unbounded. 
I have tried using partial integration $\int fg dx = Fg - \int Fg'dx$ with $f=ln(x)$ and $g = \frac{1}{(1+x)^2}$ and the other way around but I couldn't make it work. 

It is enough to use repeated integration by parts to get
$$ \int\frac{\log x}{(1+x)^2}\,dx = C +\log(x)-\frac{\log x}{1+x}-\log(1+x). $$
Differentiation under the integral sign is another viable alternative to get the same.
