$\int_{-4}^{4} \log \left(\frac{8-x}{8+x}\right) d x=$

Let $f: \mathbb{R} \rightarrow \mathbb{R}$ and $g: \mathbb{R} \rightarrow \mathbb{R}$ be continuous functions. Then the value of the integral $\int_{-\frac{\pi}{2}}^{\frac{\pi}{2}} [f(x)+f(-x)][g(x)-g(-x)] \, dx$ is

$\int_0^{3 \pi / 2} \frac{\cos ^3 x}{\cos ^3 x+\sin ^3 x} d x=$

The value of the integral $\int_{-1}^{1}\left\{\frac{x^{2015}}{e^{\mid x \mid}\left(x^{2}+\cos x\right)}+\frac{1}{e^{\mid{x} \mid}}\right\} d x$ is equal to

If $\int \limits_0^1 \frac{1}{\left(5+2 x -2 x ^2\right)\left(1+ e ^{(2-4 x)}\right)} dx =\frac{1}{\alpha} \log _{ e }\left(\frac{\alpha+1}{\beta}\right)$ where $\alpha, \beta > 0$,then $\alpha^4-\beta^4$ is equal to:

Let $f : R \to R$ be a function such that $f(2 - x) = f(2 + x)$ and $f(4 - x) = f(4 + x)$,for all $x \in R$. If $\int_{0}^{2} f(x) dx = 5$,then the value of $\int_{10}^{50} f(x) dx$ is: