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?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definite integral to evaluate

**Physics Forums | Science Articles, Homework Help, Discussion**