Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving Integral using Residues

  1. Feb 12, 2009 #1
    I've already posted this question, but I think I need to clarify my approach to the problem.

    I'm trying to solve this integral using the method of residues.

    [tex]\int_{\text{yo}}^{\text{ys}} \frac{1}{\sqrt{c+e^{-y}+y}} \, dy[/tex]

    First I've changed variables to so that

    [tex]w=\text{ArcTanh}\left[\frac{-2 y+\text{yo}+\text{ys}}{\text{yo}-\text{ys}}\right][/tex]

    and now the integral reads

    [tex]\int_{-\infty }^{\infty } \frac{\text{ys} \text{sech}^2(w)-\text{yo} \text{sech}^2(w)}{2 \sqrt{c+e^{\frac{1}{2} (\text{yo} \tanh (w)-\text{ys} \tanh (w)-\text{yo}-\text{ys})}+\frac{1}{2} (\text{yo} (-\tanh (w))+\text{ys} \tanh (w)+\text{yo}+\text{ys})}} \, dw[/tex]

    I not really sure how to find the poles or how to proceed from here....

    I think there is a pole at [tex]\left\{\left\{w = \text{ArcTanh}\left[\frac{2 c+\text{yo}+\text{ys}-2 \text{ProductLog}\left[-e^c\right]}{\text{yo}-\text{ys}}\right]\right\}\right\}[/tex]

    Any help would be appreciated
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?