How can I integrate this rational function using partial fractions?

In summary, the conversation discusses the integration of \frac{\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1} using partial fractions. The speaker is unsure which method to use but suggests trying a trigonometric substitution. Another person suggests completing the square and using the (a+b)(a-b) formula to break up the denominator. It is noted that integrating using partial fractions may be tedious.
  • #1
demersal
41
0

Homework Statement


[tex]\int[/tex][tex]\frac{\frac{1}{3}x+\frac{2}{3}}{x^{2}-x+1}[/tex]

Homework Equations



This is the result of a partial fraction integration. I don't think a direct u-substitution will work or an integration by parts.

The Attempt at a Solution



I don't know which I should use! We learned so many and none seem to work nicely in this case. Should I try to do a trigonometric substitution? That is my best guess, but since there is no radical I have no idea how to implement it!

Any sort of hint would be great. I'm just not "seeing it" ;)
 
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  • #2
Complete the square of the denominator then break it up using (a+b)(a-b) = a^2 - b^2. From here you can do it by partial fractions, though it appears tedious.
 

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