Evaluate $$\int \frac{dx}{\sin{x}-\cos{x}} $$
I know it can be done by Weierstrass substitution. But I am looking for new/simple approach. For example I tried:
$$\int \frac{1}{\sin{x}-\cos{x}} \cdot \frac{\sin{x}+\cos{x}}{\sin{x}+\cos{x}}dx=\int \frac{\sin{x}+\cos{x}}{-\cos{2x}}dx ,$$ but I can't continue from here.