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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