TITLE: Evaluating :$\int\cot^{-1} (x^2+x+1)dx $
QUESTION [8 upvotes]: How to evaluate :$$\int\cot^{-1} (x^2+x+1)dx $$

REPLY [12 votes]: Hint: Use integration by parts with v=1, but before doing that note,
$\cot^{-1}(x^2+x+1)=\tan^{-1}(\frac1{x^2+x+1})=\tan^{-1}(x+1)-\tan^{-1}(x)$ which simplifies it a lot.