Math  /  Calculus

QuestionFind the integral of 1x2x+1\frac{1}{x^{2}-x+1} with respect to xx.

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Question: After substituting back uu in terms of xx, what is the final result of the integral 1x2x+1dx\int \frac{1}{x^{2}-x+1} d x?
A) 233arctan((x12)32)+C\frac{2\sqrt{3}}{3} \arctan\left(\frac{(x-\frac{1}{2}) \sqrt{3}}{2}\right) + C B) 23arctan((x12)32)+C\frac{2}{3} \arctan\left(\frac{(x-\frac{1}{2}) \sqrt{3}}{2}\right) + C C) 233arctan((x+12)32)+C\frac{2\sqrt{3}}{3} \arctan\left(\frac{(x+\frac{1}{2}) \sqrt{3}}{2}\right) + C D) 23arctan((x+12)32)+C\frac{2}{3} \arctan\left(\frac{(x+\frac{1}{2}) \sqrt{3}}{2}\right) + C
Answer: A) 233arctan((x12)32)+C\frac{2\sqrt{3}}{3} \arctan\left(\frac{(x-\frac{1}{2}) \sqrt{3}}{2}\right) + C

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