How do you integrate #int e^-xcosx# by parts from #[0,2]#?
Thus, we apply
This didn't yield anything solvable, let's integrate by parts once more, for
Applying the integration by parts formula, we get
There's nothing here we can solve, but note how our original integral showed up again.
Now, we said
So, let's plug in what we got for
Note I have not put in a constant of integration because we're going to be taking a definite integral: