Hi there-

I have a tricky question on a math worksheet that's phrased as a hypothetical problem. Basically, it says that if I take the integral of the reciprocal of a quadratic polynomial; if it produces no arctan terms, what does this say about the roots of the quadratic?

It then furthers the question and asks the same but if it produces no arctan or logarithmic terms.

I have no clue where to start with the first part, but I have noticed that reciprocals of quadratics with a double root [such as 1/(x-1)^2 ] do not produce arctan or log terms when you integrate them.

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