$\int_\limits{-1}^1 \frac{x^3+|x|+1}{x^2+2|x|+1} d x$ is equal to

$\int\limits_0^{1 \cdot 5}\left[x^2\right] d x$ is equal to

The value of the integral $\int_0^{\pi / 2} \log \left(\frac{4+3 \sin x}{4+3 \cos x}\right) d x$ is

Let $f(x)=\max \{x+|x|, x-[x]\}$, where $[x]$ stands for the greatest integer not greater than $x$. Then $\int\limits_{-3}^3 f(x) d x$ has the value