The value of $\int_0^\pi\left|\sin ^3 x\right| \mathrm{d} x$ is

$$ \int_0^1 \log (x+1) d x= $$

$$ \int\limits_0^1 x\left|x-\frac{1}{2}\right| \mathrm{d} x= $$

$$ \int_0^{\frac{\pi}{2}} \frac{300 \sin x+100 \cos x}{\sin x+\cos x} d x=\ldots $$