𝘶-Substitution essentially reverses the chain rule for derivatives. In other words, it helps us integrate composite functions.

Using u-substitution to find the anti-derivative of a function. Seeing that u-substitution is the inverse of the chain rule.

Performing u -substitution with definite integrals is very similar to how it's done with indefinite integrals, but with an added step: accounting for the limits of integration. Let's see what this means by finding ∫ …

Find indefinite integrals that require using the method of 𝘶-substitution.

When using 𝘶-substitution in definite integrals, we must make sure we take care of the boundaries of integration.

Before diving into our practice exercise, gain some risk-free experience performing 𝘶-substitution.

A common challenge when performing 𝘶-substitution is to realize which part should be our 𝘶.

U substitution is like the reverse chain rule. When we used the derivative chain rule, we saw that d/dx f (u (x)) = df (u)/du*du/dx. U substitution exploits this pattern in evaluating indefinite integrals.

Performing u -substitution with definite integrals is very similar to how it's done with indefinite integrals, but with an added step: accounting for the limits of integration. Let's see what this means by finding ∫ …

Given an integral that should be found using u-substitution, determine what u should be.