Evaluate

\( \displaystyle \large \int^{\frac{1}{\sqrt{3}}}_{\frac{-1}{\sqrt{3}}} \dfrac{x^4}{1-x^4}\cdot \cos^{-1}(\dfrac{2x}{1+x^2}) \mathrm{dx}\)

If it can be expressed as

\(\displaystyle \dfrac{\pi}{a}\ln(b+\sqrt{c}) +\dfrac{\pi^{d}}{e} - \dfrac{\pi}{\sqrt{f}}\)

Then Find

\(\large \text{abcdef} + 1\)

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