The following integral came up in a paper I was reading recently.(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_0^{2\pi}\ln(1 + x^2 - 2x\cos\theta)d\theta [/tex]

The answer, for x^2<1, is zero. I'm not sure why. I tried writing it as a power series and showing that the integral for any given power of x vanishes, but it got too messy to work through. Anyone have a trick?

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# Definite integral to evaluate

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