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Can't reproduce a solution found in a paper using Mathematica


This is what I want to solve:

J \!\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(b\)]\(
\*SubsuperscriptBox[\(\[Integral]\), \(0\), \(a\)]
\(\*FractionBox[\(\[Rho]\ J\), \(2\ t\)]\)[x \((a - x)\) -
\*SuperscriptBox[\(a\), \(2\)]\),
SuperscriptBox[\(\[Pi]\), \(3\)]] \(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 0\), \(\[Infinity]\)]
\*SuperscriptBox[\((2  m + 1)\), \(-3\)]\ *\
\*FractionBox[\(\((2  m + 1)\) \[Pi]\ y\), \(a\)]]\), \(Cosh[
\*FractionBox[\(\((2  m + 1)\) \[Pi]\ b\), \(a\)]]\)]\ *\ Sin[
\*FractionBox[\(\((2  m +
              1)\) \[Pi]\ x\), \(a\)]]\)] \[DifferentialD]x \

...and this is the solution that I found in a publication:

(\[Rho] J^2)/(2 t)*[(a^3 b)/6 - (16 a^4)/\[Pi]^5 \!\(
\*UnderoverscriptBox[\(\[Sum]\), \(m = 0\), \(\[Infinity]\)]\(
SuperscriptBox[\((2  m + 1)\), \(-5\)] Tanh[
\*FractionBox[\(\((2  m + 1)\) \[Pi]\ b\), \(a\)]]\)\)]

I am simply not able to reproduce that with Mathematica. The obvious
questions is: why? If someone would be willing to have a look at the
the paper I could sent it over. I may say that the paper dated back
from the 70's and at that time Mathematica wasn't available (people
were smart at that time!!!! lol)

Thanks again,

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