Section 6.3: Integration by Parts

Integration-by-Parts Formula

∫ u dv = uv - ∫ v du

Integration by Parts: Selection of u and dv

For ∫ u dv = uv - ∫ v du,

1. The product u dv must equal the original integrand.
2. It must be possible to integrate dv (preferably by using standard formulas or simple substitutions).
3. The new integral ∫ v du should not be more complicated than the original integral ∫ u dv.
4. For integrals involving x^pe^ax, try:

   u = x^pand dv = e^ax dx

5. For integrals involving x^p(ln x)^q, try:

   u = (ln x)^qand dv = x^p dx