$\int_{\pi / 11}^{9 \pi / 22} \frac{d x}{1+\sqrt{\tan x}} = $

If $f(t) = \int_0^t \tan^{(2n-1)} x \, dx$,$n \in N$,then $f(t+\pi) =$

$\int_{\pi /6}^{\pi /3} \frac{dx}{1 + \sqrt{\tan x}} = $

For any real number $x$,let $[x]$ denote the greatest integer less than or equal to $x$. Let $f$ be a real-valued function defined on the interval $[-10, 10]$ by $f(x) = \begin{cases} x - [x], & \text{if } [x] \text{ is odd} \\ 1 + [x] - x, & \text{if } [x] \text{ is even} \end{cases}$. Then the value of $\frac{\pi^2}{10} \int_{-10}^{10} f(x) \cos(\pi x) dx$ is:

If $f:R \to R$ and $g:R \to R$ are one-to-one,real-valued functions,then the value of the integral $\int_{-\pi}^{\pi} [f(x) + f(-x)][g(x) - g(-x)] \, dx$ is

If $f(\alpha) = \int_{1}^{\alpha} \frac{\log_{10} t}{1+t} dt, \alpha > 0$,then $f(e^{3}) + f(e^{-3})$ is equal to.