Determine whether the integral converges or diverges. If it converges, evaluate the integral. $(5$ po$.$ each$)$

$($a$)$

${\displaystyle \underset{1}{\overset{}{}}}\frac{1}{x^{\frac{1}{3}}}dx$

$($b$)$

${\displaystyle \underset{3}{\overset{5}{}}}\frac{1}{\sqrt[\phantom{2}]{x-3}}dx$