What is integration by parts?

Integration by parts is a particular type of integration used when there are 2 functions multiplied together. There is a general formula to use: Integral of (u)dv = uv - integral of vdu. This formula will make much more sense with an example, but the gist of it is that if you're able to split up the question you've been given into 2 smaller functions you know how to differentiate and integrate, you can solve any question using the formula.