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

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

$$\int_0^1 x(1-x)^5 d x=\ldots \ldots$$

If $\int_0^a \sqrt{\frac{a-x}{x}} d x=\frac{K}{2}$, then $K=\ldots .$.