Универсальная подстановка
tg(x/2)=t
x/2= arctgt
x=2arctgt
dx=2dt/(1+t^2)
sinx=2t/(1+t^2)
cosx=(1-t^2)/*(1+t^2)
3cosx+sinx-2=3*(1-t^2)/(1+t^2) + 2t/(1-t^2)-2)=(3-3t^2+2t-2-2t^2)/(1+t^2)
∫ dx/(3cosx+sinx-2)= ∫ 2dt/(1-5t^2+2t)=-(2/5) ∫ dt/(t-(1/5)^2-6/25)=
=(-2/5)*(5/2sqrt(6))ln|(t-sqrt(6/25))/(t+sqrt(6/25)|+C=
[b]=(-1/sqrt(6))ln|(5tg(x/2)-sqrt(6))/(5tg(x/2)+sqrt(6))|+C[/b]