Mathematics

The key is to rewrite the denominator $\cos x - \sin x$ as a single sinusoidal function using the amplitude-phase form. Factor out $\sqrt{2}$ to get $\sqrt{2}\cos(x + \pi/4)$, which transforms the integral into a standard form solvable by the Weierstrass substitution $t = \tan(x/2)$. This substitution converts the trigonometric integral into a rational function that yields a logarithm with a specific argument.

The key is to rewrite the denominator $\cos x - \sin x$ as a single sinusoidal function using the amplitude-phase form. Factor out $\sqrt{2}$ to get $\sqrt{2}\cos(x + \pi/4)$, which transforms the integral into a standard form solvable by the Weierstrass substitution $t = \tan(x/2)$. This substitution converts the trigonometric integral into a rational function that yields a logarithm with a specific argument.