Exercise $2(20$ points$)$

Evaluate

$L\{e^{3t}(9-4t10sin(2t))\}$

Possible Answers

$($a$.)\frac{1}{s-3}(\frac{9}{s}-\frac{4}{s^2}\frac{20}{s^{2}4})$

$($b$.)\frac{9}{s-3}-\frac{4}{(s-3{)}^2}\frac{10}{(s-3{)}^{2}4}$

$($c$.)\frac{9}{s-3}-\frac{4}{(s-3{)}^2}\frac{20}{(s-3{)}^{2}4}$

$($d$.)\frac{9}{s3}-\frac{4}{(s3{)}^2}\frac{20}{(s3{)}^{2}4}$

$($e$.)$ None of the above

Show your work.