Happy Birthday Rajdeep!

Calculus Level 5

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

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


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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