a$)$ Use Matlab to integrate the function ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{2x^3-4x^2-x-3}{x^2-2x-3}dx$

b$)$ Use Matlab to do polynomial long division

$=>sym{(}^{\text{'}}{x}^{\text{'}})$

$=>p=2^{**}{x}^3-4^{**}{x}^2-x-3$

$=>q=x^2-2^{**}x-3$

$=>[Q,R]=$quarem$(p,q)$

$Q=2x$

$R=5x-3,F=Q+\frac{R}{q}$

$,f=2x+\frac{5x-3}{x^2-2x-3}$

c$)$ Now do the division by hand

$(\frac{2x}{x^2-2x-3})\frac{2x}{2x^3-4x^2-x-3}$

$\frac{2x^3-4x^2-5x}{5x-3}$

$\frac{2x^3-4x^2-x-3}{x^2-2x-3}=2x+\frac{5x-3}{x^2-2x-3}$

e$)$ Now find the coefficients by hand

d$)$ Now use Matlab to find the

decomposition of the remaining term. $\frac{5x-3}{x^2-2x-3}$