cross-posted from: https://lemm.ee/post/34818737
Had to learn it the hard way too many times
You still have to prove that the integral exists, i.e. that from x=0 to x=∞ the integral is some number (not ∞ and not indeterminate). So it's not a total waste of time.
Edit: oh, the limits aren't ±∞ so if the function has no vertical asymptote in the range, it's a given.