$$ \int_0^{\frac{\pi}{4}}(\sqrt{\tan x}+\sqrt{\cot x}) d x= $$

The value of the integral $\int_1^2 \frac{x \mathrm{~d} x}{(x+2)(x+3)}$ is

$$ \int_{\frac{\pi}{3}}^{\frac{2 \pi}{3}} \frac{x}{1+\sin x} d x= $$

$$ \int_0^2 \frac{3 x+1}{x^2+4} d x= $$