$\int_{-3}^3 |2-x| dx =$

If $y = \sqrt{\sec x + \sqrt{\sec x + \sqrt{\sec x + \dots \infty}}} \,,$ then the value of $\int_{0}^{\pi/3} (2y - 1) \frac{dy}{dx} \, dx$ is equal to $(\sec x > 0)$ -

If $\int \limits_{\frac{1}{3}}^3 |\log_e x| dx = \frac{m}{n} \log_e \left(\frac{n^2}{e}\right)$,where $m$ and $n$ are coprime natural numbers,then $m^2 + n^2 - 5$ is equal to $............$.

$\int_0^1 \sin \left(2 \tan ^{-1} \sqrt{\frac{1+x}{1-x}}\right) d x$ is equal to :

Let $f(x) = |x - 2|$ and $g(x) = f(f(x))$,$x \in [0, 4]$. Then $\int_{0}^{3} (g(x) - f(x)) \, dx$ is equal to

$I = \int_{\pi/4}^{\pi/3} \frac{8 \sin x - \sin 2x}{x} dx$. Then