# The idealized integral

Calculus Level 5

$\large \int_1^\infty \frac{2x^3-1}{x^6 + 2x^3 + 9x^2 + 1} \, dx$

If the integral above equals to $$\frac AB \cot^{-1} \left( \frac CD \right)$$ for positive integers $$A,B,C,D$$ such that $$\gcd(A,B) = \gcd(C,D) = 1$$, evaluate $$2(A+B+C+D)$$.

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