# 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.

×