# Integration Mania Continued

Calculus Level 5

$\large \int_{-\frac1{\sqrt3}}^{\frac1{\sqrt3}} \dfrac{x^4}{1-x^4} \text{arccos} \left( \dfrac{2x}{1+x^2} \right) \, dx$

The integral above can be expressed as

$-\dfrac{\pi^A}{B} \left [ \dfrac C{\sqrt D} - \dfrac{\pi }{E} - \dfrac FG \ln \left |\dfrac{\sqrt H+ I}{\sqrt H - I} \right | \right ] ,$

where $$A,B,C,D,E,F,G,H,I$$ are all positive integers with $$D,H$$ square-free, $$B$$ minimized and $$F,G$$ coprime.

Submit your answer as the sum of products $$AB+CD+EF+GHI$$.

×