Answer
$W = x-\frac{x^2}{2L_0}+\frac{L_0^2}{L_0+x}-L_0$
Work Step by Step
We know the following equation for work:
$W=\int_0^{x}F(x)dx$
Thus, we find:
$W=\int_0^{x}F_0[\frac{L_0-x}{L_0}-\frac{L_0^2}{(L_0+x)^2}]dx$
$W=\int_0^{x}F_0[1-\frac{x}{L_0}-\frac{L_0^2}{(L_0+x)^2}]dx$
$W = x-\frac{x^2}{2L_0}+\frac{L_0^2}{L_0+x}-L_0$
