Integration by Partial Fractions with Trig Sub, Irreducible Quadratic, and Long Division

In this video, we talk about integration by partial fractions decomposition. This is an example that needs long division first before decomposing the rational function into partial fractions. In order to do the decomposition, we also need the denominator to be in factored form.

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

In this video, I used a combination of both ways!

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

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#Calculus #Integration #PartialFractionDecomposition

[cailinleahy]

Thank you, you mathematical angel. The last ten minutes of this video were invaluable to me. Many many thanks.