The interval in which f(x)=cot^-1 x+ x increases is

Given, $f(x)=\cot^{-1} x+ x$,

Differentiating both sides we get, $f'(x)=\frac{-1}{1+x^2}+1$

or $f'(x)=\frac{-1+1+x^2}{1+x^2}$ or $f'(x)=\frac{x^2}{1+x^2}$

Clearly, $f'(x)>0$ for all x.

So, $f(x)$ increasing in $(-∞,∞)$