Question

Evaluating an improper integral which results in an infinity over infinity case. It has been a few years and I can't remember how to deal with it

Answer 1

\[t * (-\frac{ 1 }{ s } * e^{-st})\]

Answer 2

when t varies from zero to infinity

Answer 3

that's the leading term in the IBP for \(\mathcal{L} \{ t\}\)?? if not, my bad.

if yes, write it as \(-\dfrac{1}{s} \dfrac{t}{e^{st}}\) and the exponential on the bottom out grows the linear on top

or apply L'Hopital as it's in indeterminate form