Answer
$\dfrac{8s+2}{s^2+2s}$
Work Step by Step
The Laplace Transform can be written as:
$L[F(t)]=\int_{0}^{\infty} e^{-st} f(t) dt $
We are given that $f(t)=7 e^{-2t}+1$
Now, $L[F(t)]=L[7 e^{-2t}+1] \\=L[7 e^{-2t}]+L[1] \\=\dfrac{7}{(s+2)}+\dfrac{1}{s}\\=\dfrac{7s+s+2}{s^2+2s}\\=\dfrac{8s+2}{s^2+2s}$
