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.

Consider the integral I=int_(0)^(2pi)(dx)/(5-2cosx) Making the substitution "tan"1/2x=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.

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