$$\oint_{|z-3|=2} \frac{\log z}{z+1} dz$$ Where $log$ denotes the natural logarithm.
I'm so confused with the fact that the function $f(z)=\frac{\log z}{z+1}$ has a singularity in $z=-1$ and the contour passes through it. I think I have to draw a new contour around this point, but appears this branch $<-\infty,0]$. Please guide trhough this problem.