# How do you integrate int e^(1/t)/t^2 by parts?

Integration by parts is a waste of time. Just use the substitution $u = \frac{1}{t}$. This implies that $\mathrm{du} = - \frac{1}{t} ^ 2 \mathrm{dt}$.
$\int {e}^{\frac{1}{t}} / {t}^{2} \mathrm{dt} = - \int {e}^{\frac{1}{t}} \frac{- 1}{t} ^ 2 \mathrm{dt} = - \int {e}^{u} \mathrm{du} = - {e}^{u} + C = - {e}^{\frac{1}{t}} + C$