I was asked to calculate the integral
$ \int_a^\infty F dr$
where $ F=\frac{k}{r}\vec{e_r}^{}$
k is a constant.
At first I thought this was pretty simple:
$ \int_a^\infty F dr= \int_a^\infty \frac{k}{r} dr=[k\ln(r)]\Big|_a^\infty$
And well this integral is undefined (infinity).
However my professor came up with the answer:
$\frac{k}{a^2}$
What am I doing wrong? Am I missing something because this is a line integral?