# To Leibniz

Calculus Level 4

$\large \int_0^\pi \dfrac{dx}{(2-\cos x)^2} = \, ?$

You are given that for constant $$a> 1$$, the equation below holds true, $\displaystyle \int_0^\pi \dfrac{dx}{a - \cos x} = \dfrac\pi{\sqrt{a^2-1}} \; .$ With this information, find the exact closed form of the integral above.