I'm solving a definite integral where one of the borne is infinity. When I try to evaluate the borne at infinity, I'm getting stuck, because I'm getting the undetermined infinity form $ 0 \cdot \infty $. Here is the integral I'm trying to evaluate (it's already solved, I just need to evaluate it).
$\left[-\frac{te^{-st}}{s} - \frac{e^{-st}}{s^2}\right]_{0^+}^{\infty}$
And when I try to evaluate it, I get :
$\left(-\frac{\infty \cdot 0}{s}\right) + \frac{1}{s^2}$
I know it's possible to modify the borne slightly to evaluate the integral, but I don't think it makes sense to evalute the integral at $\infty^-$.
Also, when I view the formula that I'm integrating, it clearly looks like it's going toward 0, so my feeling tells me that the result should be $\dfrac{1}{s^2}$, but since it's an homework I need to prove it.