Integration of Rational Function by Partial Fraction Decomposition - Irreducible Quadratic Factor

In this video, we talk about integration of rational functions by partial fraction decomposition. This is an example whose denominator has an irreducible quadratic factor. The form of the decomposition for the irreducible quadratic factor involves a linear expression Ax + B in the numerator:

(Ax + B)/(irreducible quadratic factor)

There are two methods of finding the constants in the decomposition.
1) Traditional way (by matching the coefficients)
2) Plug in convenient x-values to make terms disappear

For this problem, we use both methods.

See here for the video that I show both ways of finding the constants:

See how to integrate functions in the form of 1/(ax + b) here:

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#Calculus #Integration #PartialFractionDecomposition

[douglasablandino]

Hi, nice video btw! I'd like to know what's the name of the program that you're using for the development of the integral. I've been looking for programs like this one, so I don't have to use a sheet for my practices. It would help me so much.