# Will the ILATE rule work?

Calculus Level 5

$\large \int_{-\frac{1}{\sqrt{3}}}^{\frac{1}{\sqrt{3}}}\frac{x^{4}}{1-x^{4}}\cos^{-1}\left(\frac{2x}{1+x^{2}}\right)dx$ The closed form of the integral above is of the form $$\displaystyle \frac{\pi ^{2}}{a}-\frac{\pi }{\sqrt{b}}-\frac{\pi }{c}\ln \left(\frac{\sqrt{b}-1}{\sqrt{b}+1}\right)$$.

Find the value of $$a+b+c$$.

×