Добрый день!
Проверьте, пожалуйста, мое решение:
int 3 * cos^2 x/sin^4 x dx = 3 * int cos^2 x/(sin^2 x * sin^2 x) dx =
= 3 * int cos^2 x/sin^2 x * 1/sin^2 x dx = 3 * int cos^2 x/sin^2 x d(-ctg x) =
= -3 * int ctg^2 x d(ctg x) = | t = ctg x | = -3 * int t^2 dt =
= -3 * 1/3 * t^3 + C = -t^3 + C = | t = ctg x | = - ctg^3 x + C