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Consider the integral I=int(0)^(2pi)(dx)...

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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