Integration by parts: choose which factor is u, step through each pass of the formula and derive it from the product rule
Parts is the product rule, read backwards
Differentiate a product and you get two terms. Integrate that line and rearrange it, and you have ∫u dv = uv − ∫v du: a product swapped for a boundary term and a new integral. The whole skill is choosing u so the new integral is simpler than the one you started with. Pick which factor is u for ∫x²eˣ dx, step through the passes and watch what happens to the power of x left under the integral sign.
Parts tableStart · start
Pick the integrand and which factor is u, then step through the passes. Watch the power of x left under the integral sign.