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

If the function f is continuous at $x = \pi$, where $f(x) = \dfrac{1 - \cos[7(x - \pi)]}{5(x - \pi)^2}$, for $x \neq \pi$, then $f(\pi) = $