Delta function!

Calculus Level 5

\[ \large \displaystyle\int _{ -\infty }^{ \infty }{ { e }^{ -{ x }^{ 2 } }\delta ({ x }^{ 2 }-2)\quad \, dx } =\dfrac { A{ e }^{ -B } }{ C\sqrt [ D ]{ F } } \]

The equation above holds true for positive integers \(A,B,C,D\) and \(F\), find the minimum value of \(A+B+C+D+F+2\).

Notation: \(\delta(\cdot)\) denotes the Dirac delta function.

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