Consider the integral `int_0^(2pi)(dx)/(5-2cosx)` making the substitution `tan(x/2)=t ,` we have `I=int_0^(2pi)(dx)/(5-2cosx)` `=int_0^0(2dt)/((1+t^2)[5-2(1-t^2)/(1+t^2)])=0` The result is obviously wrong, since the integrand is positive and consequently the integral of this function cannot be equal to zero. Find the mistake.