$\int_2^3 \frac{d x}{x^2-x}$ is equal to

$\int_0^{\pi /2} \frac{\cos x}{(1 + \sin x)(2 + \sin x)} \,dx = $

The value of the integral $\int_{0}^{\frac{\pi}{2}} 60 \frac{\sin (6 x)}{\sin x} d x$ is equal to.

$\int_{-\pi / 4}^{\pi / 3}\left|\tan \left(x-\frac{\pi}{6}\right)\right| d x=$

Suppose $g(x) = \int_0^x f(t) dt$,where $f$ is such that for $t \in [0, 1]$,$0 \le f(t) \le \frac{1}{2}$ and for $t \in [1, 2]$,$\frac{1}{2} \le f(t) \le 1$. Find the range of $g(2)$.

$\int_0^{\pi / 4} \frac{d x}{\cos ^3(x) \cdot \sqrt{2 \sin (2 x)}}=$