Здравствуйте. Подскажите, пожалуйста, как найти интеграл
int sin^3 x/(1 + cos^2 x) dx
Заранее спасибо!!!

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