Laplace's Integral

$\displaystyle P_n(x)$	$\textstyle =$	$\displaystyle {1\over \pi}\int_0^pi {du\over\left({x+\sqrt{x^2-1}\cos u}\right)^{n+1}}$
	$\textstyle =$	$\displaystyle {1\over \pi}\int_0^\pi (x+\sqrt{x^2-1}\cos u)^n\,du.$