Not the Normal Distribution

Calculus Level 4

e(x2+1x2) dx=πAeB\large \int_{-\infty}^{\infty}e^{-\left(x^2+\frac{1}{x^2}\right)}\text{ }dx=\frac{\pi^A}{e^B}

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

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