2

I'm having difficulties as to evaluating the complex integral. Also, how should I use its result to evaluate the real valued integral ?

Integrate the function $$f(z) = \frac{z}{1 - a e^{-i z}} ;\: a > 1$$ around a suitable rectangle to show $$\int_0^\pi \frac{a x \sin x}{1 - 2 a x \cos x + a^{2}} dx = \pi \ln \left(1 + \frac{1}{a} \right).$$

engineeringstudent
  • 21
  • First, you should determine the singularities of $f$, and its residues there. – Julien Mar 03 '13 at 17:01
  • Thanks julien, evaluating the residue of the singularity z0=iln(1/a) and using Cauchy's integral theorem solves the complex integral however I do not know how to use this info to solve the real valued integral – engineeringstudent Mar 03 '13 at 18:01

0 Answers0