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The task is to calculate the following integral:

$$\int_{1/3}^{3}{\frac{\tan^{-1}x}{x^{2}-x+1}dx}$$

However the answer me currently getting seems to be too large and odd, any ideas of more efficient solution? P.S I was using universal substitution for rational trigonometric equations

gt6989b
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9cloudalpha
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    I would integrate by parts, differentiating the arctangent, hope to end up with a rational function. – gt6989b Feb 16 '20 at 16:28
  • @gt6989b Tried that, however the amount of calculations seems rather enormous, comparing with other problems given.. – 9cloudalpha Feb 16 '20 at 16:31

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