Integration of rational function with quadratic denominator
From Calculus
Template:Specific function class integration strategy
Contents
Outline of method
Reduction to the case where the numerator is constant or linear and the denominator is monic
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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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