The value of the integral $\int\limits_0^{\pi / 4} \frac{x \mathrm{~d} x}{\sin ^4(2 x)+\cos ^4(2 x)}$ equals :

Question

$\frac{\sqrt{2} \pi^2}{8}$

$\frac{\sqrt{2} \pi^2}{16}$

$\frac{\sqrt{2} \pi^2}{32}$

$\frac{\sqrt{2} \pi^2}{64}$

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