1. The problem statement, all variables and given/known data I need to find 2 functions on [0,1]: one that is integrable, one that isn't, such that their product is integrable. I'd like to use functions that are non-constant, if possible 2. Relevant equations 3. The attempt at a solution I was thinking of using g(x) := x-1 h(x) := 1/(x-1) ... But I'm having trouble proving h(x) is not integrable on [0,1]... I used the fact that g was monotone to prove it is integrable and obviously gh is integrable because it's constant. Right now we're looking at Riemann integrals, but I don't know how to state the proof... Please help!