Интеграл dx\(1+3cos^2x)

[latex]\int{dx\over1+3cos^2x}=\{t=tgx,dx={1\over1+t^2}\}=\int{dt\over4+t^2}={1\over2}arctg{t\over2}+C=\\={1\over2}arctg{tgx\over2}+C[/latex]