Numerical integration over a cube with a singularity – math.stackexchange.com

I am interested in numerically evaluating $g(\mathbf{r}')=\int_{D}\frac{f(\mathbf{r})}{|\mathbf{r}-\mathbf{r}'|^{\gamma}}d^3r$ with $f(\mathbf{r})$ some continuous (not necessarily analytic) ...