Find
$$
\int_{-4 \pi \sqrt{2}}^{4 \pi \sqrt{2}}\left(\frac{\sin x}{1+x^{4}}+1\right) d x .
$$
Solution: The function $\frac{\sin x}{1+x^{4}}$ is odd, so its integral over this interval is 0 . Thus we get the same answer if we just integrate $d x$, namely, $\mathbf{8} \pi \sqrt{\mathbf{2}}$.