OUESTION $8[25]$

$8\mathrm{.}1$ Determine the following integrals by making use of tables where possible:

$8\mathrm{.}1\mathrm{.}1{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}{x}^2{e}^{-3x}dx,($Integration by parts$)$

$8\mathrm{.}1\mathrm{.}2{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x+1}{4x^2-4x+1}dx,($Partial fractions$)$

$8\mathrm{.}1\mathrm{.}3{\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{x-3}{2x^2-3x-2}dx,($adjustment of the numerator$)$

$8\mathrm{.}2$ Sketch and the curve of $y=-x^2+3x+4$ and $y=\frac{4x}{3}$ on the same set of axes. Clearly indicate the intersection points between the curve and the line. Hence, calculate the area enclosed between the curves