How to integrate $\tan(x) \tan(2x) \tan(3x)$? We have to integrate the following
$$\int \tan x \tan 2x \tan 3x \,\mathrm dx$$
In this I tried as
First split it into sine and cosine terms
Then used $\sin 2x =2\sin x \cos x$
But after that got stuck

Notice
$$\tan3x=\frac{\tan2x+\tan x}{1-\tan2x\tan x}\Rightarrow \tan3x\tan2x\tan x=\tan3x-\tan2x-\tan x$$
then
$$\int \tan3x\tan2x\tan x \mathrm{d}x = \int \tan3x - \tan2x - \tan x \ \mathrm{d}x$$
the answer will follow.
