$$\int_\limits0^{\frac{\pi}{2}} \log \left[\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\right] d x=$$

$$\int_0^{\frac{\pi}{2}} \sqrt{\cos \theta} \cdot \sin ^3 \theta d \theta=$$ ............

$$\int_{\frac{\pi}{18}}^{\frac{4 \pi}{9}} \frac{2 \sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x=\ldots \ldots$$

$$\int_\limits a^b \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a+b-x}} d x=\ldots \ldots$$