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.