You need to break the integral into 3 contours to avoid the singularity at 0.

the first is a line from $\large (-1-\imath) \to \epsilon e^{-\imath \frac{3\pi}{4}}$

the second is a semicircle of radius $\epsilon$ from $\large \epsilon e^{-\imath \frac {3 \pi}{4}} \to \epsilon e^{\imath \frac {\pi}{4}}$

the third is a line from $\large \epsilon e^{\imath \frac {\pi}{4}} \to (1+\imath)$

you should be able to formulate these contours and integrate. Use partial fractions to break up the integrand into recognizable pieces. Take the limit as $\epsilon \to 0$