What is L$1(1$s$2+4$s$+13)\backslash$displaystyle $\backslash$mathcal$\{$L$\}^\{-1\}\backslash !\backslash$Bigl$(\backslash$tfrac$\{1\}\{$s$^2+4$s $+13\}\backslash$Bigr$)$L$1($s$2+4$s$+131)?$

Choices:

A$.13$e$3$tsin$(2$t$)\backslash$tfrac$\{1\}\{3\}$e$^\{-3$t$\}\backslash$sin$(2$t$)31$e$3$tsin$(2$t$)$

B$.$ e$2$tsin$(3$t$)$e$^\{-2$t$\}\backslash$sin$(3$t$)$e$2$tsin$(3$t$)$

C$.13$e$2$tsin$(3$t$)\backslash$tfrac$\{1\}\{3\}$e$^\{2$t$\}\backslash$sin$(3$t$)31$e$2$tsin$(3$t$)$

D$.13$e$2$tsin$(3$t$)\backslash$tfrac$\{1\}\{3\}$e$^\{-2$t$\}\backslash$sin$(3$t$)31$e$2$tsin$(3$t$)$