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∫1∞2x3−1x6+2x3+9x2+1 dx \large \int_1^\infty \frac{2x^3-1}{x^6 + 2x^3 + 9x^2 + 1} \, dx ∫1∞x6+2x3+9x2+12x3−1dx
If the integral above equals to ABcot−1(CD) \frac AB \cot^{-1} \left( \frac CD \right) BAcot−1(DC) for positive integers A,B,C,DA,B,C,DA,B,C,D such that gcd(A,B)=gcd(C,D)=1 \gcd(A,B) = \gcd(C,D) = 1 gcd(A,B)=gcd(C,D)=1, evaluate 2(A+B+C+D)2(A+B+C+D) 2(A+B+C+D).
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