Consider the function $f$ defined by $$f(x)=\int_0^{2\pi}\ln\left(x^2-2x\cos t+1\right) \,dt.$$
I tried calculating values of this function using Wolfram Alpha and I observed that $f(x)=0$ for all $x\in[-1,1]$. How can we prove this fact?
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user437713
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Another one: https://math.stackexchange.com/q/352046/42969 – Martin R Mar 12 '20 at 18:17
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@MartinR thanks I searched math.stack before posting but I didn't found something similar. Can I ask how did you found it. Thanks again!! – user437713 Mar 12 '20 at 18:21
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With Approach0 – See also https://math.meta.stackexchange.com/questions/24978/announcing-a-third-party-search-engine-for-math-stackexchange on Meta. – Martin R Mar 12 '20 at 18:22
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@MartinR thanks a lot. That really helps!!! – user437713 Mar 12 '20 at 18:25