Question

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

Answer 1

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