Some integrals with problematic evaluation

[quinyu]

Same with the 1/(4-cos(x)^2). After our rewrite u=tan(x), we get 1/(3+4x^2). From there, the previous rule applies, giving x/(2sqrt(3))+atan(sin(x)cos(x)/(3+2sqrt(3)+sin(x)^2))/(2sqrt(3)).