# Let's do some calculus! (15)

Calculus Level 3

$\large \displaystyle \int_{-\infty}^{\infty}{\dfrac{e^{-x^{2}}}{\sqrt{\pi}}} \,dx - e^{i \pi} = ~ ?$

Notations:

• $e \approx 2.71828$ is the Euler's number.
• $i = \sqrt{-1}$ is the imaginary unit.

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