$$ \int\limits_{\frac{-\pi}{2}}^{\frac{\pi}{2}}\left(x^2+\log \left(\frac{\pi-x}{\pi+x}\right) \cdot \cos x\right) d x= $$

$$ \int_0^1 \log \left(\frac{1}{x}-1\right) d x= $$

The value of $\int_0^1 \tan ^{-1}\left(1-x+x^2\right) \mathrm{d} x$ is

$$ \int_3^5 \frac{\sqrt{x} \mathrm{~d} x}{\sqrt{8-x}+\sqrt{x}}= $$