(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm trying to evaluate

[tex]\int_0^{2\pi} \frac{9-6\cos t}{5-4\cos t} dt \ .[/tex]

I found that the antiderivative of the integrand is

[tex]F(x) = \frac{3}{2}x + \tan^{-1} \left(3\tan\frac{x}{2} \right)[/tex]

so using the FTC, the integral should be

[tex]F(2\pi)-F(0)=3\pi[/tex]

But using a calculator to evaluate the integral yields [itex]4\pi[/itex].

What am I doing wrong here?

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Having problems evaluating definite integral

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