$$\int_\limits{\frac{\pi}{6}}^{\frac{\pi}{2}} \frac{\operatorname{cosec} x \cdot \cot x}{1+\operatorname{cosec}^2 x} d x=$$

$$\int_\limits0^2|2 x-3| d x=$$

If $$\int_\limits0^a \sqrt{\frac{a-x}{x}} d x=\frac{k}{2}$$, then $$k=$$

$$\int\limits_5^{10} \frac{d x}{(x-1)(x-2)}=$$