Happy Birthday Rajdeep!

Calculus Level 5

1/31/3x2(1x2)(ex+1)(1+x2)4dx\large \int_{-1/\sqrt{3}}^{1/\sqrt{3}} \dfrac{x^2(1-x^2)}{(e^x+1)(1+x^2)^4} \, dx

If the above integral is equal to ab \dfrac{\sqrt{a}}{b}, where aa and bb are positive integers with aa square-free, find a+ba+b.


This problem is original and was inspired by one of Trevor B's problems. This problem is dedicated to Rajdeep on his birthday.
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