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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 '20 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? $\endgroup$ Jan 15 '20 at 11:49
  • $\begingroup$ What are the restrictions on the parameters? $\endgroup$ Jan 15 '20 at 11:49
  • $\begingroup$ They are all positive real number. $\endgroup$ Jan 15 '20 at 12:02
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    $\begingroup$ Have you already tried throwing it into Wolfram Alpha to see what happens? $\endgroup$ Jan 15 '20 at 12:41

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