Помогите, пожалуйста, найти интеграл
int 1/sin^4 x dx

int 1/sin^4 x dx = int 1/sin^2 x * 1/sin^2 x dx = int 1/sin^2 x d(-ctg x) =
= -int 1/sin^2 x d(ctg x) = -int (1 + ctg^2 x) d(ctg x) = | ctg x = t | =
= -int (1 + t^2) dt = -(t + 1/3 * t^3) + C = -t - 1/3 * t^3 + C =
= | t = ctg x | = -ctg x - 1/3 * ctg^3 x + C

Спасибо.