A calculus problem by Jonas Katona

Calculus Level 3

\[\large I=\int _{ -\infty }^{ \infty }{ \dfrac { { x }^{ 2 } }{ { x }^{ 4 }+4 } } \, dx\] If \(I\) can be expressed in the form \(\dfrac { \pi }{ a }\), find \({ a }^{ a }\).

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