$\int_0^{2a} f(x) dx - \int_a^{2a} f(x) dx =$

$\int_0^1 \frac{8 \log (1+x)}{1+x^2} \,d x=$

$\int_2^8 \frac{5^{\sqrt{10-x}}}{5^{\sqrt{x}}+5^{\sqrt{10-x}}} d x$ is equal to

$\int_0^{\pi / 2} \frac{1}{1+\tan ^{2020}(x)} d x=$

$\int_{-\pi}^{\pi} \frac{\sin^4 x}{\sin^4 x + \cos^4 x} \, dx = $

The value of the integral $\int_{-2}^{2} \frac{\sin^2 x}{[\frac{x}{\pi}] + \frac{1}{2}} \, dx$ (where $[x]$ denotes the greatest integer less than or equal to $x$) is