I need some help with the integral
\begin{align} \vec{\nabla }\times \left[ \frac{1}{4\pi\varepsilon } \int \frac{\rho \big( \hspace{0.375ex}\vec{r}\hspace{0.25ex}' \hspace{0.01ex}\big)}{\big\| \hspace{0.375ex}\vec{\eta}\hspace{0.1ex}^{2}\hspace{0.125ex} \big \|}\;\vec{\eta}\,dv\right ] \end{align}
where $\;\vec{\eta}=\vec{r}-\vec{r}\hspace{0.1ex}'$.
This entire thing looks like a mess. Some help would be ideal.