Use Of Partial Fraction? Really?

Calculus Level 4

\[ \large \int_0^\infty \dfrac{x^2(12x^2 - 1)}{(4x^2 + 1)^3 (1+x^2)} \, dx = \dfrac \pi A \]

If the equation above holds true for some constant \(A\), find \(A\).

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