I came across a question today...
Integrate $\int \dfrac{\sin x-\cos x}{(\sin x+\cos x)\sqrt{(\sin x \cos x + \sin^2x\cos^2x)}}\,dx$
How to do it? I tried
1. to take $\sin x \cos x =t$ but no result
2. to convert the thing in the square root into $\sin x +\cos x$ so that I could take $\sin x + \cos x = t$ but then something I got is $\int\frac{-2}{t|t+1|\sqrt{t-1}}\,dt$. Now I don't know how to get past through it.