a$.$ Integrate the following function analytically and using the trapezoidal rule, with $n=1,2,3$ and $4.$

${\displaystyle \underset{1}{\overset{2}{}}}(x+\frac{2}{x}{)}^{2}dx$

b$.$ Integrate the following function analytically and using Simpson's $\frac{1}{3}$ rule, with $n=4$ and $5$

${\displaystyle \underset{-3}{\overset{5}{}}}(4x-3{)}^{3}dx$