Question

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

Answer 1

Integration by parts is a waste of time. Just use the substitution `u=1/t`. This implies that `du=-1/t^2dt`.

`inte^(1/t)/t^2dt=-inte^(1/t)(-1)/t^2dt=-inte^udu=-e^u+C=-e^(1/t)+C`