Question

найти неопределенный интеграл ​

Answer 1

Ответ:

$\int\limits \frac{ \cos(2x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } dx = \int\limits \frac{ \cos {}^{2} (x) - \sin {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } dx= \\ = \int\limits \frac{ \cos {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } dx - \int\limits\frac{ \sin {}^{2} (x) }{ \cos {}^{2} (x) \sin {}^{2} (x) } dx = \\ = \int\limits \frac{dx}{ \sin {}^{2} (x) } - \int\limits \frac{dx}{ \cos {}^{2} (x) } = - ctgx - tgx + C$