Chapter 8.3, Problem 80E

Verifying a Reduction Formula In Exercises 79-82, use integration by parts to verify the reduction formula. (A reduction formula reduces a given integral to the sum of a function and a simpler integral.)

${\displaystyle \int {\cos }^{2}xdx=\frac{{\cos }^{n-1}x\sin x}{n}+\frac{n-1}{n}{\displaystyle \int {\cos }^{n-2}xdx}}$