The original math can be found here Original Derivation.
My question is how does one derive expression (9)? In other words the equation $$v({\textbf{r}})={f \over{8\pi \eta r}}[\textbf{e}+(\hat{r} \cdot \textbf{e})\hat{r}]$$ where $r=|\textbf{r}-\textbf{r}_0|$ and $\hat{r}={(\textbf{r}-\textbf{r}_0) \over r}$. We are given the expression
$$v(\textbf{r})=\int O(\textbf{r-r}')\textbf{f}(\textbf{r}')d^3x'$$ where the Oseen tensor $O(\textbf{r})={1\over 8\pi\eta}({1\over|\textbf{r}|}I+{\textbf{r}\otimes \textbf{r} \over|\textbf{r}|^3})$ and $\textbf{f}=f\textbf{e}\delta(\textbf{r}-\textbf{r}_0)$. I think the confusion lies in the integral itself, and how exactly that integral equals expression (9) after substitution of the other things in?