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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.

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

J. M.'s missing motivation
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  • Your question might already be answered by this or this question. – Thies Heidecke Aug 03 '17 at 11:01
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    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. – Wen Chern Aug 03 '17 at 14:57
  • To add to @Wen's comment, if you use Limit[] at the end, pay special attention to the Direction option. – J. M.'s missing motivation Aug 04 '17 at 05:26

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