The value of $\cot^{-1}\left[\dfrac{\sqrt{1 - \sin x} + \sqrt{1 + \sin x}}{\sqrt{1 - \sin x} - \sqrt{1 + \sin x}}\right]$, where $x \in \left(0, \dfrac{\pi}{2}\right)$ is...

If $(\tan^{-1}x)^2 + (\cot^{-1}x)^2 = \dfrac{5\pi^2}{8}$, then the value of $x$ is equal to...

If $f\left(\dfrac{x-1}{x+1}\right) = x + 1$, then $\int f(x)\,dx = \cdots$

If $e^x + e^{f(x)} = e$, then the domain of $f(x)$ is