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Given that $\int_{-\infty}^{\infty} e^{-x^2/2} dx = \sqrt{2 \pi}$, what is the value of $\int_{- \infty}^{\infty} \mid x \mid ^{-1/2} e^{- \mid x \mid} dx$?

  1. $0$
  2. $\sqrt{\pi}$
  3. $2 \sqrt{\pi}$
  4. $\infty$
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