When I integrate by parts how do I know which part of the equation is u and v'?

To determine which function is your u value in the by parts equation, you can use the acronym LATE to find the order of precedence for this value. LATE stands for: Logarithmic functions Arithmetric functions Trigonometric functions Exponential functions This order is down to how easy it is to integrate each function, with logs being the most difficult and exponentials being the easiest. For example, if you were told to integrate xln(2x), u would be ln(2x) in this case because it is much easier to differentiate that to get u' (1/x) than it would be to integrate it.