Non Standard Integral int(1/(a-b*cos(x),x)

int(1/(a-b*cos(x),x) types of integral can be readily solved using the substitution tan(x/2) = u. Which gives cos(x) = 2 *(cos(x/2))^2-1 = (u^2-1)/(u) and du = 1/2*(sec(x/2)^2*dx and change of variable gives 2*du/(1+u^2) = dx and substitutin^2+1g for dx and cos(x) in the original integral int(1/(a-b*cos(x),x) in terms of u is now a breeze !