Worksheet $6$

Write a Python function$/$script that performs the following tasks.

Use Romberg integration the computes an approximation to: ${\displaystyle \underset{0}{\overset{1}{}}}\frac{2x}{x^2+e}dx.$

$($a$)$ Determine $R_{4,4}($use at least eight digits in the approximation$)$

$($b$)$ Display $R_{1,2},R_{2,1},$dots,$R_{4,4}$ in table form.

$($c$)$ Compare $R_{4,4}$ with the exact solution.