# Another "messy" integral

$\int_0^\pi \! log(1-2tcos(x)+t^2) \, \mathrm{d} x$
you can integrate by parts dv = dx , and $\log (1-2t\cos x + t^2 ) = u$
after that you can use the substitution $u = \tan \frac{x}{2}$ to the solve the resulting integral