The function $f(x) = \tan^{-1}(\sin x + \cos x)$ is an increasing function in the interval.....

The minimum value of $\dfrac{\log x}{x}$ in the interval $(2, \infty)$ is

$\displaystyle\int \dfrac{(x + 1)(x + \log x)^2}{x}\,dx =$

$\displaystyle\int \cot^4 x\,dx$ is equal to