A calculus problem by Hung Woei Neoh

Calculus Level 3

π/4π/4x2tanx1+cos4xdx=?\large \int_{-\pi/4}^{\pi/4} \dfrac{x^2 \tan x}{1+ \cos^4 x} dx= \, ?


Source: My high school friend's college calculus course practice question set.
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