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How to evaluate the following integral: $\int\limits_1^2{\dfrac{\arctan{x}}{x^2-x+1}dx}$?

I tried to make a substitution $t = \arctan{x}$, but it didn't help.

Any help would be appreciated.

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  • $\begingroup$ According to WA it cannot be evaluated in terms of elementary functions. A very complicated-looking answer. $\endgroup$ – David Quinn Jun 2 '15 at 9:16
  • $\begingroup$ Why was the feynman trick answer deleted? $\endgroup$ – grdgfgr Jun 2 '15 at 9:45

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