Integration by Parts Integration by parts handles products by trading derivatives: ∫u dv=uv−∫v du.\int u\,dv = u v - \int v\,du.∫udv=uv−∫vdu. For definite integrals: ∫abu dv=[uv]ab−∫abv du\displaystyle \int_a^b u\,dv = [u v]_a^b - \int_a^b v\,du∫abudv=[uv]ab−∫abvdu. PreviousSubstitution (Integration) NextIntegrals of Rational Functions