Integration by Parts
Integration by parts is a method for solving complex integrals.
Contents
Description
Given a complex integral, refactor it as ∫udv. The problem can then be rewritten as:
Derivation
The formula derives from the product rule:
Take the integral of both sides and breaking up the RHS into a sum of two integrals. Allowing for the improper notation, this can be written as:
The LHS obviously reduces to uv. The RHS further simplifies by rewriting in terms of the derivatives, creating differentials.
This trivially can be rewritten into the familiar form above.