Isn’t it nice how calculus takes something that complex and makes it simple?
Well, for our next integration method, Partial Fraction Decomposition, we are going to learn how to integrate any rational function (algebraic fraction), by expressing it as a sum of simpler fractions..
Partial Fractions is an integration technique that allows us to break apart a “big, hard” fraction into “smaller, easier” fractions.
Purple Math explains that partial-fraction decomposition is the process of starting with the simplified answer and retaking it apart, or “decomposing” the final expression into its initial polynomial fractions.
We will walk through 5 examples in depth, where we’ll explore:
- How to handle Partial Fractions given linear factors.
- How to work problems with repeating and non-linear factors.
- How to use long division to first simplify our Integrand prior to applying Partial Fractions.
Example of Integration by Partial Fractions
We will use two different approaches to simplifying each fraction (i.e., plugging in factors and the comparison method), and we will see how Integration by Partial Fractions utilizes all of our previously learned integration skills to simplify expressions.
As always, we will review our integration techniques and determine the best order of how to “attack” any integration problem.
Partial Fraction Decomposition Video
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