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How do you go about integrating the reciprocal of a quadratic when it cannot be factorised (ruling out the use of partial fractions)?

E.g.

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

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    Of course every quadratic can be factored --- over the complex numbers. Then you can use partial fractions. Unfortunately, the answer you get will involve nonreal numbers, too, but some of us don't mind that.2012-10-25

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