I've just found that, for all a>0:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int_0^\infty \frac{a (x^2 - 1)^2 - 2 x (x + a)^2}{(x + a)^3 (a x + 1)^3} dx = 0[/tex]

This can be found by brute force, but there must be a simpler way to show it.

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# Why is this integral zero

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