
hello professor integration by parts: so what does it mean exactly when you have integral of df(x)/dx dx ? Does it just mean differentiate f(x) to get another function then integrate that with respect to x? But can the dx on the top and bottom not cancel?
Yes, that's what it means. And you, you can't cancel top and bottom. The Leibniz notation may look like a fraction but it's not a fraction. It's a <em>limit</em> of a fraction.

