$1) \int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}}\frac{\sqrt[3]{sin^3x-sin x}}{sin x}cot x dx$
$2) \int\limits_{0}^{\frac{\pi}{2}}(\sqrt[3]{cos x}-\sqrt[3]{sin x})dx$
$3) \int\limits_{0}^{\frac{\pi}{2}}\frac{4cos x - 3sin x + 1}{4sin x + 3cos x + 5}dx$
$4)
\int\limits_{0}^{2} \frac{x}{\sqrt{2 + x} + \sqrt{2 - x}}dx$