$\int_{0}^{1} \log \left(\frac{1}{x}-1\right) d x$ is equal to

The integral $\int_0^\pi \frac{8 x \, dx}{4 \cos^2 x + \sin^2 x}$ is equal to

Let $f(x) = \frac{\sin x}{x}$,then $\int_{0}^{\frac{\pi}{2}} f(x) f\left(\frac{\pi}{2} - x\right) dx =$

Evaluate $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}} \sin^{2} x \, dx$

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:

$\int_{\frac{\pi}{5}}^{\frac{3 \pi}{10}} \frac{\tan x}{\tan x + \cot x} \, dx =$