Answer
$\frac{x}{2}+\frac{\sin2x}{4}+C$
Work Step by Step
Recall:
$\cos 2x= 2\cos^{2}x-1$ or $\cos^{2}x= \frac{1+\cos2x}{2}$
We have,
$\int \cos^{2}xdx= \frac{1}{2}\int (1+\cos2x)dx$
$=\frac{1}{2}\int dx+\frac{1}{2}\int \cos 2xdx$
$=\frac{x}{2}+\frac{\sin2x}{4}+C$
