Definite Integral from 0 to 2 Pi of Logarithm of a plus b Cosine x

Theorem

 * $\ds \int_0^{2 \pi} \map \ln {a + b \cos x} \rd x = 2 \pi \map \ln {\frac {a + \sqrt {a^2 - b^2} } 2}$

where:
 * $b$ is a real number
 * $a$ is a positive real number with $a \ge \size b$.