Polarize it

Calculus Level 4

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

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