Not the Normal Distribution

Calculus Level 4

\[\large \int_{-\infty}^{\infty}e^{-\left(x^2+\frac{1}{x^2}\right)}\text{ }dx=\frac{\pi^A}{e^B}\]

Find \(100(A+B),\) where \(A\) and \(B\) are rationals such that the equation above is fulfilled.