$[$Section $5\mathrm{.}5]$ Find the consumer and producer surpluses using the demand function $p=-0\mathrm{.}05x+36$ and supply function $p=0\mathrm{.}2x+16,$ where $p$ is the price $($in dollars$)$ and $x$ is the number of units $($in thousands$).$ Start by solving for the equilibrium point. $(17$ points$)$

$[$Section $6\mathrm{.}1]$ Use integration by parts to find the indefinite integral ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}x\sqrt[4]{x+7}dx.(8$ points$)$