Partial Fractions | Repeating and irreducible Quadratic Terms

While in the Intro to Partial Fractions video we largely focused on decomposing rational functions whose denominators were products of non-repeating linear terms, in this video we investigate what happens if the factors are either repeating or irreducible quadratics (i.e. they can not be factored into the product of two linear terms using real numbers).

This might make the algebra more complicated, but it is effectively the same process as before: hypothesize a decomposition with undetermined coefficients, break up the equation into a system of equations you can solve, and then integrate the result. The final integrals are doable, but can sometimes take a bit of work (a u-sub or identifying the derivative of arctan(x) ).

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. #calculus #math

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