I have this function,

$$F(r) = \frac{1}{r^{6}-1+i 0^{+}}$$

I don't know how to specify a function like this in Mathematica. The problem is how to specify the infinitesimal small imaginary part. This imaginary part is added to make the following integral possible without affecting from the singularity at 1.

And my next question is how to evaluate following integral in Mathematica.

$$\int_{-1}^{1} \frac{1}{r^{6}-1+i 0^{+}}dr$$

  • $\begingroup$ Your question might already be answered by this or this question. $\endgroup$ Commented Aug 3, 2017 at 11:01
  • 3
    $\begingroup$ If you are doing numerical calculation, you can just add to the denominator a small (instead of infinitesimal) imaginary part. If you are doing analytic calculation, a possible (but maybe not the best) way is to add to the denominator a imaginary part $$i\epsilon$$, and take the limit $$\epsilon\to0$$ after integration. $\endgroup$
    – Wen Chern
    Commented Aug 3, 2017 at 14:57
  • $\begingroup$ To add to @Wen's comment, if you use Limit[] at the end, pay special attention to the Direction option. $\endgroup$ Commented Aug 4, 2017 at 5:26


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