The value of $\int_{a}^{b} \frac{x}{|x|} dx$,where $a < b < 0$,is

The integral $\int_{0}^{\frac{\pi}{2}} \frac{1}{3+2 \sin x+\cos x} d x$ is equal to.

If $I = \int_0^{100\pi} \sqrt{1 - \cos 2x} \, dx$,then the value of $I$ is

$\int_0^\pi |\cos x| \, dx = $

If the value of the integral $\int_{0}^{5} \frac{x+[x]}{e^{x-[x]}} \,dx = \alpha e^{-1} + \beta$,where $\alpha, \beta \in R, 5\alpha + 6\beta = 0$,and $[x]$ denotes the greatest integer less than or equal to $x$; then the value of $(\alpha + \beta)^{2}$ is equal to:

$\int_{1/e}^e |\log x| \, dx = $