$(20$ points$)$ Consider the integral ${\displaystyle \underset{2}{\overset{4}{}}}\frac{dx}{(x-2{)}^{\frac{3}{2}}}.$

$($a$)$ Why is this an improper integral?

$($a$)$

$($b$)$ Determine if the integral converges or diverges. If it converges, compute its value.

$($b$)$