Let

$I_n={\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{7^2}{(7^2+x^2{)}^n}dx,n=2,3,$dots

$($a$)$ Find $g(x)$ such that

$I_n=\frac{1}{7^2}{I}_{n-1}+{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{g(x)}{(7^2+x^2{)}^n}dx$

and enter it in the box below using Matlab syntax.

$g(x)=$

Syntax advice: Remember that for Matlab syntax you must have $*$ for multiplication, for example $\frac{2}{3}x+x^2$

should be entered as $\frac{2}{3}*x+x^2$

$($b$)$ By evaluating the integral on the right hand side of $($a$)$ with $g(x)$ that you found, find $A_n$ and $B_n$ such that

$I_n=A_n{I}_{n-1}+B_n\frac{x}{(7^2+x^2{)}^{n-1}}$

Enter $A_n$ and $B_n$ below using Matlab syntax.

$A_n=$

$B_n=$ PLEASE DO PART B