Methods to integrate this integral:
$$\int \cot(5x) \tan(2x) \mathrm{d}x$$
I have tried several methods, step by step, and they have led to invalid results. Helpful hints or processes are welcome.
I did this further :
$$ \cot(5x) = \frac{1}{\tan(2x+ 3x)}$$ $$= \frac{1}{\frac{\tan 2x +\tan 3x}{1-\tan 2x\tan 3x}}$$
Simplifying it further by breaking $\tan(3x) = \tan(2x +x)$ again we get $$= \frac{1-\tan^2 x -2\tan x \tan 2x}{2\tan 2x -\tan^2 2x . \tan x +\tan x}$$
now the integral is $$ = \frac{1-\tan^2 x -2\tan x \tan 2x}{2\tan 2x -\tan^2 2x . \tan x +\tan x} \tan 2x $$
Can we do something with this further thanks..