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What’s the proper way to typeset a differential operator?

What formatting should I use on 'd' when writing an integral?

I normally use

$$\int_{-\infty}^{infty} e^{-x^2} \mathoperator{d}\!x = \pi$$

which produces

$\int_{-\infty}^{infty} e^{-x^2} dx = \pi$

Is there a better formatting for dx?

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