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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 \
\[DifferentialD]r23\)\)\)

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.

2  
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