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Have you guys ever needed to define Integrate boundaries as equations?

I tried to submit the equation as was written in original text but it seems that mathematica can't understand it.

kb = 0.001872041; Na =  6.02214129*10^23;
ep = 10.22; p = 2.56;

pot2[r_] := 4 ep ((p/r)^12 - (p/r)^6)

f[r_, T_] := Exp[-pot2[r]/(kb T)] - 1
    B3[T_] := -8 \[Pi]^2/3  Na^2 \!\(
\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(\[Infinity]\)]\(
\*UnderoverscriptBox[\(\[Integral]\), \(Abs[r12 - r13]\), \(r12 + 
       r13\)]f[r12, T]\ f[r13, T]\ f[r23, 
       T]\ r12\ r13\ r23\ \[DifferentialD]r12 \[DifferentialD]r13 \

Original Text

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closed as off-topic by xzczd, RunnyKine, Yves Klett, MarcoB, m_goldberg Apr 14 at 13:41

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "The question is out of scope for this site. The answer to this question requires either advice from Wolfram support or the services of a professional consultant." – xzczd, RunnyKine, Yves Klett, MarcoB
If this question can be reworded to fit the rules in the help center, please edit the question.

Perhaps you should try to find the real culprit Integrate[ x y z, {x, 1, 2}, {y, -x, x^2}, {z, x - y, x + y}] – Dr. belisarius Jul 2 '13 at 12:44
As mentioned by @Dr.belisarius , what's incorrect here is the original text. (Or at least it has followed a very uncommon rule for the order of integration variables.) Anyway, Abs[r12 - r13], r12 + r13 can only be bounds of r23. – xzczd Apr 14 at 6:21
I'm voting to close this question as off-topic because the issue it raises is not a Mathematica issue but a mathematical one. That it is formulated in terms of Mathematica is not sufficient to make it an appropriate question for Mathematica.SE. – m_goldberg Apr 14 at 13:41