Answer
The proof is below.
Work Step by Step
Work is equal to the integral of power with respect to time. Thus, we find:
$W=\int P dt$
$W=\int_0^{\infty} (\frac{P_0t_0^2}{t+t_0^2}) dt$
$W=((\frac{-P_0t_0^2}{(t+t_0^2)^2})|_0^{\infty}$)
We know that the infinite limit of the equation is $-P_0t_0^2$, so we know that the magnitude of the work done as time approaches infinity is $P_0t_0^2$.
