Answer
$\frac{5s}{s^2+4}-\frac{7}{s+1}-\frac{3.6!}{s^7}$
Work Step by Step
Given: $f(t)=5\cos 2t-7e^{-t}-3t^6$
Using the Convolution Theorem
$L[F(s)]=L[5\cos 2t-7e^{-t}-3t^6]\\
=5L[\cos 2t]-7L[e^{-t}]-3L[t^6]\\
=\frac{5s}{s^2+4}-\frac{7}{s+1}-\frac{3.6!}{s^7}$
