I am trying to find the integral of $\int \frac{\cos x+\sin 2x}{\sin x}$
$\int \frac{\cos x}{\sin x} + \int \frac{\sin 2x}{\sin x}$
$\int \tan x + \int \frac{\sin 2x}{\sin x}$
I think I am suppose to have the integral of tanx memorized so I will put that to the side for now.
$\int \frac{\sin 2x}{\sin x}$
I do not know what to do with this since I can't make a u subsitution or anything else so I will just randomly use the double angle identity I have memorized.
$\int \frac{2\sin x\cos x}{\sin x}$
$\int 2\cos x$
$2 \int \cos x$
$2\sin x + \int \tan x$
$2\sin x + \ln|\sec x| + c$
This is of course wrong.