# Gaussian integral 2016, Part II

Calculus Level 4

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

Hence or otherwise, evaluate the integral

$\large \int_{-\infty}^{+\infty} e^{-x^2 + 2x + 2016} \, dx$

If the above integral can be expressed in the form $a e^{b} \sqrt{\pi}$, where $a , b$ are positive integers, find $a+b$.

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