$$\int_0^a \sqrt{\frac{x}{a-x}} d x=$$

$$\int_\limits2^3 \frac{x}{x^2-1} d x=$$

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

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