Chapter 14.7, Problem 5P

The values of the following integrals are known and can be found in integral tables or by computer. Your goal in evaluating them is to learn about contour integration by applying the methods discussed in the examples above. Then check your answers by computer.

${\displaystyle {\int }_0^{\pi }\frac{d\theta }{1-2r\cos \theta +r^2}}(0\le r<1)$