Integration by Parts — Overview

Integration by parts undoes the product rule for derivatives. It is used whenever the integrand is naturally a product of two functions of different kinds — a polynomial times a trigonometric function, a logarithm times a power of $x$, and so on — where differentiating one factor and integrating the other repeatedly simplifies the problem. The sections below state the theorem, explain how to choose which factor to differentiate (the LIATE rule), and then apply the method to several important families: integrals of inverse-trig/log functions alone, integra …