# Gaussian integral 2016, Part I

Calculus Level 4

The Gaussian integral states that $$\displaystyle \int_{-\infty}^{+\infty} e^{-x^2 } \, dx = \sqrt{\pi }$$.

Given that information (if it is related at all to this problem), evaluate the integral

$\displaystyle \int_{- \infty}^{+\infty} e^{-\frac{25}{9} (x+2016)^{2}} \, dx$

If the integral above can be expressed in the form

$\dfrac{a}{b} \sqrt{\pi }$

with $$a, b$$ as positive coprime integers, find $$a+b$$.

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