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How to integrate? $$\int{ \frac{\arctan\sqrt{n^{2}-1}}{\sqrt{n^{2}+n}}} dn$$

I have no idea how to do it. Tried to get some information from wiki, but its too hard :|

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Please try to use a more specific title, this one is very generic and will not assist users searching for similar queries in future. – Simon Hayward Dec 1 '12 at 21:10
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It's easier for people if you use conventional letters for variables. Since only one variable appears in your question, it would be more friendly to call it $x$. The letter $n$ normally denotes an integer. – John Bentin Dec 1 '12 at 21:24
The substitution $n=\sec\theta$ looks messy. I've also gotten it into the form $\int\frac{\cos^{-1}xdx}{x\sqrt{x+1}}$ and tried integration by parts, but that doesn't seem to lead anywhere as eliminating the inverse trig function still leaves natural log terms... – Mike Dec 2 '12 at 18:16
@user51402 looks like Wolfram Mathematica refuses symbolic integration. – Caran-d'Ache May 18 at 8:19

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