Integrating the following function – math.stackexchange.com

I am asked to evaluate the integral $$\int_{R^n}e^{-\sum_{i=1}^na_i^2x_i^2}\,dx$$ given that $a_1,a_2,\cdots,a_n$ are real numbers different from $0$. I am clueless on how to approach this, since I ...

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