Question

Интеграл dx / (sin^2(x) - 5sin(x)cos(x))

Answer 1

$\large \int \frac{dx}{sin^2x-5sinxcosx}=\int\frac{dx}{sin^2x(1-5ctgx)}=\frac{1}{5}\int\frac{d(1-5ctgx)}{1-5ctgx}=\\=\frac{1}{5}ln|1-5ctgx|+C$