$(5$pts$)$ Consider the series below.

${\displaystyle \underset{i=1}{\overset{}{}}}\frac{1}{(k+2)(k+3)}=\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}+\frac{1}{56}+\frac{1}{72}+$cdots

Find the first five partial sums $S_1,S_2,S_3,S_4$ and $S_5$ of the series. Then find a formula for the nth partial sum $S_n,$ and determine the value of the series, if possible.

$(4pts$ Use an appropriate technique to evaluate the following integral.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{9-2x}{\sqrt[\phantom{2}]{36-25x^2}}dx.$