Step 1 We notice that the integrand in (x - 2) (x + 3)5 dx is a product. We need a Product Rule for Integration, and while we don't have exactly that, we have integration by parts. udv = uv - / v . du We have two obvious choices for u: x - 2 and (X + 3). Looking at the integration formula, we note that the power of u will be one less. That could be useful on both terms, but with one, lowering the power will get rid of the term entirely. This suggests that we should choose u = x - 2 and dv = dx. X