Question

$\int \frac{dx}{\cos 3x-\cos x}=$

Answer 1

$\int \frac{dx}{-2\sin 2x\sin x}$

$=\int \frac{dx}{-4\cos x{\sin }^{2}x}$

$=\frac{-1}{4}\int \frac{{\sin }^{2}x+{\cos }^{2}xdx}{\cos x{\sin }^{2}x}$

$=\frac{-1}{4}\int \left(\sec x++\cos ecx\cot x\right)dx$

$=\frac{-1}{4}\left[\log \left|\sec x+\tan x\right|\right]$

$=\frac{-1}{4}\left[\log \left|\sec x+\tan x\right|-\cos ecx\right]+c$