I've already posted this question, but I think I need to clarify my approach to the problem.(adsbygoogle = window.adsbygoogle || []).push({});

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Solving Integral using Residues

Can you offer guidance or do you also need help?

**Physics Forums | Science Articles, Homework Help, Discussion**