Найдите неопределенный интеграл: [latex] \int\limits \frac{cos2xdx}{sin^2xcos^2x}[/latex]

[latex] \int \dfrac{\cos2xdx}{\sin^2x\cos^2x}= \int \dfrac{\cos^2x-\sin^2x}{\sin^2x\cos^2x}dx= \\\\\ = \int \dfrac{\cos^2x}{\sin^2x\cos^2x}dx-\int \dfrac{\sin^2x}{\sin^2x\cos^2x}dx= \\\\\ =\int \dfrac{1}{\sin^2x}dx-\int \dfrac{1}{\cos^2x}dx=-\mathrm{ctg}x-\mathrm{tg}x+C[/latex]