#### Answer

$W = (0.632)~L~F_0$

#### Work Step by Step

We can find the work that the force does on the particle as it moves from x = 0 to x = L
$W = \int_{0}^{L}~F_x~dx$
$W = \int_{0}^{L}~F_0~e^{-x/L}~dx$
$W = -L~F_0~e^{-x/L}~\Big\vert_{0}^{L}$
$W = (-L~F_0~e^{-L/L})-(-L~F_0~e^{-0/L})$
$W = (-L~F_0~\frac{1}{e})-(-L~F_0)$
$W = L~F_0~(1-\frac{1}{e})$
$W = (0.632)~L~F_0$