Integration of kf'(𝑥)[f(𝑥)]ⁿ Using u - Substitution (Year 13, Chapter 11 Supplemental)

u-substitutions can also be used when integrating problems that are also sometimes known as "reverse chain rule" problems. Many textbooks and teachers will advocate the "reverse chain rule" method, which relies on spotting what form the integrated function would have been in "by inspection", and then adjusting for any constants.

Don't get me wrong - this method is brilliant, slick and intuituive. However, sometimes it may take a little time to get the stage where you can "see" what to do using this inspection method, and also, some integrals can be written so awkwardly that it can make integration by inspection rather difficult.

Another approach that will always work, instead of by inspection, is to introduce a u-substitution, and this is the method I focus on here. I would suggest to students to try both methods, but to start with using u-substitutions.

Introduction and theory: 0:00
Why I teach this method: 10:30

Worked Examples: 13:38