Chapter 5.5, Problem 112E

sin² ax and cos² ax integrals Use the Substitution Rule to prove that

$\begin{array}{l}{\displaystyle \int {\sin }^{2}axdx}=\frac{x}{2}-\frac{\sin (2ax)}{4a}+C\text{and}\hfill \\ {\displaystyle \int {\cos }^{2}axdx}=\frac{x}{2}+\frac{\sin (2ax)}{4a}+C.\hfill \end{array}$