Answer
See below
Work Step by Step
Given: $F(s)=\frac{1}{s+1}\\
G(s)=\frac{1}{s}$
Obtain: $L^{-1}[F(s)* G(s)]=L^{-1}[\frac{1}{s+1}.\frac{1}{s}]\\
=L^{-1}[\frac{1}{s+1}].L^{-1}[\frac{1}{s}]\\
=e^{-t}.1\\
=\int^t_0 e^{-(t-x)}dx\\
=e^{-t}\int^t_0 e^x dx\\
=e^{-t}\begin{bmatrix}
e^x
\end{bmatrix}^t_0\\
=1-e^{-t}$
