How to evaluate this expression: $∫\frac{\sin2x}{(1 - \cos2x)^4}\:\mathrm{d}x$? 
How to evaluate: $$∫\frac{\sin2x}{(1 - \cos2x)^4}\:\mathrm{d}x$$ If anyone knows the answer, please help.


Note that $\cos 2x=\cos^2 x-\sin^2 x$ so $1-\cos 2x=2\sin^2 x$ and $\sin 2x =2\sin x \cos x$. So you end up integrating $$\frac {2\sin x\cos x}{(2\sin^2 x)^4}=\frac {\cos x}{8\sin^7 x}$$
Then if we substitute $y=\sin x$ then we can write $dy = \cos x dx$
