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$\large \int _{ -\infty }^{ \infty }{ \frac { { x }^{ 2 } }{ ({ x }^{ 2 }+4)^{ 3 } } } \, dx$

The integral shown above can be written as $\dfrac { \pi }{ { A }^{ 2 } }$. Find the value of $|A|$.

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