Question

Evaluate $\int \cos x\cos 2xdx$

Answer 1

$\begin{array}{c}I=\int \cos x\cos 2xdx\\ I=\int \frac{2}{2}\cos 2x\cos xdx\\ I=\frac{1}{2}\int \left[\cos \left(2x+x\right)+\cos \left(2x-x\right)\right]dx\\ I=\frac{1}{2}\int \left(\cos 3x+\cos x\right)dx\\ I=\frac{1}{2}\left[\frac{\sin 3x}{3}+\frac{\sin x}{1}\right]+c\end{array}$

Hence, this is the answer.