Approximate the definite integral using Simpson's rule for the given value of $n.$ Give the result accurate to $3$ decimal places.

$($a$){\displaystyle \underset{3}{\overset{4}{}}}\frac{1}{x+1}dx,n=8$

$$

$($b$)$ Find the upper bound for the absolute value of the error based on $|f^{(4)}(x)|$ and Theorem $2.($Round the decimal value to three decimal places.$)$

$|E_S|0\mathrm{.}032,vv{10}^{-6}$

$($c$)$ Find the exact value of the definite integral.