L{e^{-t}} = int _0 to infinty [e^{st}*e^{2-t} dt = int _0 to infinty [e^{st}*e^{2} *e^{-t}dt = e^{2} int _0 to infinty [e^{(s-1)t} dt L{e^{-t}} = e^2/(s+1) Solution L{e^{-t}} = int _0 to infinty [e^{st}*e^{2-t} dt = int _0 to infinty [e^{st}*e^{2} *e^{-t}dt = e^{2} int _0 to infinty [e^{(s-1)t} dt L{e^{-t}} = e^2/(s+1).