If $\frac{1}{x^4+1}=\frac{A x+B}{x^2+\sqrt{2} x+1}+\frac{C x+D}{x^2-\sqrt{2} x+1}$, then $B D-A C=$

$$ \int \frac{2 x^2 \cos x^2-\sin x^2}{x^2} d x= $$

If $\int \frac{\log \left(1+x^4\right)}{x^3} d x=f(x) \log \left(\frac{1}{g(x)}\right)+\tan ^{-1}$ $(h(x))+c$, then $h(x)\left[f(x)+f\left(\frac{1}{x}\right)\right]=$