I would like to prove that(adsbygoogle = window.adsbygoogle || []).push({});

##\displaystyle{\int dx'\ \frac{1}{\sqrt{AB}}\exp\bigg[i\frac{(x''-x')^{2}}{A}\bigg]\exp\bigg[i\frac{(x'-x)^{2}}{B}\bigg]=\frac{1}{\sqrt{A+B}}\exp\bigg[i\frac{(x''-x)^{2}}{A+B}\bigg]}##

Is there an easy way to do this integration that does not involve squaring the brackets?

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# I Gaussian integration for complex phase

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