Let's suppose we wish to calculate:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] PV \int_{0}^{\infty}dx\frac{e^{-sx}}{1-x} [/tex] (1)

I don't know how to do it, my idea is take the identity:

[tex] \frac{1}{1-x}=1+x+x^{2}+x^{3}+............ |x|<1 [/tex]

[tex] \frac{1}{1-x}=-x^{-1}-x^{-2}-x^{-3}+x^{3}+............ |x|>1 [/tex]

So (1) using Cauchy's principal value, is the same as to calculate with a positive small epsilon:

[tex] \int_{0}^{1-\epsilon}dxx^{k} e^{-sx} [/tex]

[tex] \int_{1+\epsilon}^{\infty}dxx^{-k} e^{-sx} [/tex]

and calculate term by term integration to get the Principal value of (1)

**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!

# Evaluating this integral (Principal value)

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

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