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Here is an integral which I don't know the answer:

$$\int^1_0 \frac{dx}{x^2+x+1}$$

I tried to use complex number to solve i.e. the root of $x^2+x+1$ is $(-1/2 + \sqrt {3}i/2)$. Let w=$(-1/2 + \sqrt {3}i/2)$ , then it becomes $ \int_{0}^{1} 1/(x-w)^2\,\mathrm{d} (x-w)$ , the answer is in terms of complex number. I wanna ask whether my method is correct and seek for another method. Thank you.

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    Let $x=u-\dfrac12$. This is equivalent to "completing the square" of the quadratic in your denominator. Remember what the derivative of the arctangent looks like.2012-07-17

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