Evaluate the following integrals:

$($a$)$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2\sqrt[\phantom{2}]{x^{3}3}dx$

$($b$)$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{1}{\sqrt[\phantom{2}]{64-x^2}}dx$

$($c$)$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}(43x)e^{3x}dx$

$($d$)$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{5}{x^2-x-6}dx$

$($e$)$

$I={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}xsi{n}^{-1}xdx$