As usual, I have a tricky question. There is an integral that Maple can take numerically
R0 := 1/(a-sqrt(b+c*cos(x)));
Now let's put the coefficients, e.g.
a := 0.9; b := 4.5; c :=0.1
and take the integral from 0 to 2*Pi
R1 := evalf(int(R0, x = 0 .. 2*Pi));
Also, there is an exact analytical result that Maple gives (I give it after simplifying it to avoid division by zero for the limit x=0 and x=2*Pi)
As it turns out, the results are completely different. In the first case -5.145818656, while for the second case -3.612771378+0.I
Moreover, If we change the coefficients to a := 0.9; b := 4.5; c := -4 then I obtain Float(undefined)+3.662506136*I and -2.362349457+3.662506117*I , respectively.
My question: how to avoid this descepancy?