I need help computing $\int {\ln x\over 2-x}\, dx$

Let $x=2-2t$ and use $\int \frac{\ln(1-x)}{x}dx=-\text{Li}_2(x)+C$ $$\int {\ln x\over 2-x}dx=-\int \frac{\ln 2+\ln(1-t)}{t}dt=-\ln 2 \ln t +\text{Li}_2(t)+C$$