Answer
See below
Work Step by Step
Given: $f(t)=7te^{-t}$
Obtain: $F(s)=\int^{\infty}_0 e^{-st}f(t)dt\\
=\int^{\infty}_0 e^{-st} (7te^{-t})dt\\
=7\int^{\infty}_0 te^{-(s+1)t}dt\\
=7[\lim (\frac{-t}{s+1}e^{-(s+1)t})]^n_0+\frac{1}{s+1}\int^n_0 e^{-(s+1)t}dt\\
=\frac{7}{(s+1)^2}$
