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. 

Partial integration actually works:
$$\int \frac{\log(x)}{(1+x)^2}dx=-\frac{\log(x)}{(1+x)}+\int\frac{1}{x(1+x)}dx$$
and this last one you can easily solve by writing
$$\frac{1}{x(1+x)}=\frac1{x}-\frac{1}{1+x},$$
thus one obtains
$$\int \frac{\log(x)}{(1+x)^2}dx=-\frac{\log(x)}{(1+x)}+\log(x)-\log(1+x)+C$$
