The function y = x-cot^-1x-log(x+√((x^2+1))) is increasing on

We have, $y = x-\cot^{-1}x-\log(x+\sqrt{(x^2+1)})$

$⇒\frac{dy}{dx}=1+\frac{1}{1+x^2}-\frac{1}{\sqrt{1+x^2}}=\frac{(\sqrt{1+x^2}-1)}{(1+x^2)}+1≥0$ for all x

Thus, the given function is increasing for all x ∈ (−∞, ∞)