Помогите, пожалуйста, найти интеграл
int 1/(1 + cos^2 x) dx

int 1/(1 + cos^2 x) dx = int 1/(cos^2 x * (1 + 1/cos^2 x)) dx =
= int 1/(1 + 1/cos^2 x) d(tg x) = int 1/(1 + tg^2 x + 1) d(tg x) =
= | tg x = t | = int 1/(2 + t^2) dt =
= | t = 2^(1/2) * u, u = t/2^(1/2), dt = 2^(1/2) du | =
= int 1/(2 + 2 * u^2) * 2^(1/2) du = 2^(1/2)/2 * int du/(1 + u^2) =
= 1/2^(1/2) * arctg u + C = | u = t/2^(1/2) | = 1/2^(1/2) * arctg (t/2^(1/2)) + C =
= | t = tg x | = 1/2^(1/2) * arctg (tg x/2^(1/2)) + C

Спасибо (IMG:style_emoticons/default/smile.gif)