If $f(x)=\left|\begin{array}{ccc}2 \cos ^2 x & \sin 2 x & \sin x \\ \sin 2 x & 2 \sin ^2 x & -\cos x \\ \sin x & -\cos x & 0\end{array}\right|$, then

$$ \left.\int_0^{\pi / 4}|2| f(x) \mid+5 f^{\prime}(x)\right) d x= $$

$\int_0^3\left(\sin \left(\frac{\pi}{3} x\right)-\cos \left(\frac{\pi}{3} x\right)\right) d x=$

$$ \int_0^{\pi / 2} \sin ^4 \theta \cos ^3 \theta d \theta= $$

It is given that $\frac{d}{d t}(t \log t-t)=\log t$, then $\exp \left(\int_0^1 2 x \log \left(1+x^2\right) d x\right)=$