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Sorry it's bit abrupt, but recently I am caught up in some symbolic calcualtion which is tedious and almost impossible with mere human hands, so just wondering is it possible to solve the double integral of what's written below using Matlab or some other platform?

$$\int_{0}^{a}dk\frac{1}{k}\int_{|k-q|}^{|k+q|}dk'\frac{1}{k'}(k^2+q^2-k'^2)(k'^2+q^2-k^2)(k'^2-(k+q)^2)(k'^2-(k-q)^2)[\frac{1}{v_F(k-k')-w}+\frac{1}{v_F(k-k')+w}].$$

And to clarify, all the variables are positive real numbers. The first integral is about $k'$ with upper and lower limit being $|k+q|$ and |k-q| respectively, and second integral is about $k$ from $0$ to $a$. The symbols other than $k$ and $k'$ can all be seen as real positive constants.

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  • $\begingroup$ That certainly looks like the sort of hairy integral an algebra system might be able to help with, yes. It depends on what the $[[\cdots]]$ notation means and what $v_f$ is rather a lot though. I'd suggest you try it. $\endgroup$ – tfb Jan 15 at 10:59
  • $\begingroup$ @tfb thanks a lot! I just realized [[]] is a mistake which is in fact the square bracket. Do you think it's still possible to do the integral? $\endgroup$ – Xinxin Peng Jan 15 at 11:49
  • $\begingroup$ What are the restrictions on the parameters? $\endgroup$ – Alex Trounev Jan 15 at 11:49
  • $\begingroup$ They are all positive real number. $\endgroup$ – Xinxin Peng Jan 15 at 12:02
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    $\begingroup$ Have you already tried throwing it into Wolfram Alpha to see what happens? $\endgroup$ – Federico Poloni Jan 15 at 12:41

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