$$ \int_0^2 x^8\left(\frac{4}{x^2}-1\right)^{\frac{5}{2}} d x= $$

$$ \int_{-\pi / 2}^{\pi / 2} \sin ^2 x \cos ^2 x(\sin x+\cos x) d x= $$

$$ \int_{1 / 5}^{1 / 2} \frac{\sqrt{x-x^2}}{x^3} d x= $$

$$ \int_0^{400 \pi} \sqrt{1-\cos 2 x} d x= $$