Using LaTeX, evaluate the integral \[ \int_C{\frac{\vec{r}}{|\vec{r}|^3} ds} \] where the curve $C(s)$ is the straight line between vectors $\vec{a}$ and $\vec{b}$, parameterized by $0 \leq s \leq 1$.
Here's how you can solve that problem using LaTex:
\begin{equation*}
\begin{split}
  I &= 
    \oint_\mathcal{L}{\frac{\vec r}{|\vec r|^3}}\,ds \\&=
     \int^1_{0}\left[(\cos t -t)\hat a + (\sin t) \hat b\right]\cdot d \hat r \, dt = \pi[\cos(1)-1+0\times 0]=2\pi 
\end{split} 
\end{equation*}
The last equality holds since we chose our parametrized path to go from vector $\mathbf{a}$ to zero. The result of evaluating your integral would then be two pi.