Q$7(10$ points$)$

Compute the following improper integrals.

${\displaystyle \underset{0}{\overset{8}{}}}\frac{1}{x^{\frac{1}{3}}}dx$

${\displaystyle \underset{0}{\overset{8}{}}}\frac{1}{x}dx$

${\displaystyle \underset{0}{\overset{8}{}}}\frac{1}{x^2}dx$

Consider the function ${\displaystyle \underset{0}{\overset{b}{}}}\frac{1}{x^p}dx,$ where $p$ and $b$ are positive numbers. Using parts $($a$)-($c$)$ to create an argument for what values of $p$ the integral has a finite solution.