In Mathematica 12.3: Integrate[Log[1 - 2 a Cos[x] + a^2], {x, 0, Pi}, Assumptions -> Abs[a] >= 1 && a \[Element] Reals] gives the correct answer -\[Pi] Log

In Mathematica 12.3: Integrate[Log[1 - 2 a Cos[x] + a^2], {x, 0, Pi}, Assumptions -> Abs[a] >= 1 && a \[Element] Reals] gives the correct answer -\[Pi] Log[1/a^2]