Integral $\int \frac{\cos x }{2+\sin 2x} dx$ I have tried to find antiderivative of
$$ \frac{\cos x\  }{2+\sin 2x} $$
using the variable change $t= \cos x -\sin x$ with sin $\sin2x=2\sin x\cos x $. But i don't come up to its closed-form result as shown below.
How can I find its antiderivative? Thanks in advance


Try  $$\sin x= \frac {2\tan x/2}{1+\tan ^2 x/2}$$
$$\cos x= \frac {1-\tan ^2 x/2}{1+\tan ^2 x/2}  $$
and $$u= \tan (x/2)$$
$$du=( 1+\tan^2 (x/2))dx $$
