8 .3 • IMPROPER. !NTEGR.ALS OF RATIONAL FUNCTIONS 309- EXAMPLE 8.15 Evaluate J::oo (:e•+i'i<o:•+w
Solution We write the integrand as f (z) = (z+i)(z-i)(~+ 2 i)(z- 2 i). We see that
f has simple poles at the points i and 2i in the upper half-plane. Computing