Integration of rational function with quadratic denominator

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Template:Specific function class integration strategy

Outline of method

Reduction to the case where the numerator is constant or linear and the denominator is monic

Fill this in later

Case that the denominator has distinct linear factors

UPSHOT: The antiderivative in this case is expressible as a linear combination with constant coefficients of the natural logarithms of the absolute values of the linear factors.

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Case that the denominator has repeated linear factors

UPSHOT: The antiderivative in this case is a constant divided by the linear factor plus a constant times the natural logarithm of the linear factor.

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Case that the denominator has negative discriminant

UPSHOT: The antiderivative in this case is a constant times an arc tangent function plus a constant times the natural logarithm of the absolute value of the quadratic.

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