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 $|A|$ .