Integration by Substitution
For differentiation we had special rules like chain rule, product rule, and quotient rule. Since integration is the inverse process of differentiation, it seems reasonable to conclude that special rules exist for integration. One special rule we will study for integration is called substitution, commonly called u-substitution. Integration by substitution allows us to recover functions that required the chain rule to take its derivative.
The basic strategy of u-substitution is to find one part of the integral that 'looks like' the derivative of another part. We then substitute the variable u for one part, and du for the other (the derivative part). There are usually 'tipoff’s' that we would like to u-sub. One in particular is the presence of two polynomials within the integrand, which differ in degree by 1.
Learn more about integration by substitution by reading the explanation below.
Practice: Use the substitution method to integrate functions in the following exercises.