HMMT 2001 K10

Evaluate the definite integral $\int_{-1}^{+1} \frac{2 u^{332}+u^{998}+4 u^{1664} \sin u^{691}}{1+u^{666}} \mathrm{~d} u$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{2}{333}\left(1+\frac{\pi}{4}\right)

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