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

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

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

$$ \int_0^{2 a} f(x) d x= $$