Polarize it

Calculus Level 4

x2(x2+4)3dx\large \int _{ -\infty }^{ \infty }{ \frac { { x }^{ 2 } }{ ({ x }^{ 2 }+4)^{ 3 } } } \, dx

The integral shown above can be written as πA2\dfrac { \pi }{ { A }^{ 2 } } . Find the value of A|A| .

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