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The tricky thing about partial fractions is that there are four kinds of partial fractions problems. The kind of partial fractions decomposition you’ll need to perform depends on the kinds of factors in your denominator.
You can have 1) Distinct linear factors, 2) Distinct quadratic factors, 3) Repeated linear factors, or 4) Repeated quadratic factors. You can also have a mix of any and all of these.
In this video, we’re going to look at a partial fractions problem with repeated linear factors. We’ll do the partial fractions decomposition, and then use the method of undetermined coefficients to solve for our constants. Then we’ll plug these back into the decomposition, and the decomposition back into the integral, and then we’ll be able to evaluate the integral.
Remember, partial fractions in general is a method of integration that you can use to simplify rational functions to make them easier to integrate. If it’s possible to integrate the function directly, or to use u-substitution or integration by parts, those methods will all likely be easier and quicker than partial fractions, so you should consider them before you try this.
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