That's a mouthful! Some schools introduce partial fractions the first time in Algebra 2 or Pre-Calc, making it not quite so strange when you see it in Calculus. But then again, who remembers Pre-Calc?
The first two videos below don't have any integration; they're just the pre-calc videos about partial fraction decomposition. The last one is about the integration, which is pretty simple once you've already mastered decomposition! (Hint: you're going to get a lot of ln's.)
Integration by Partial Fraction Decomposition
In this video we'll go through all the ins and outs (and rules) of using partial fractions to do integrals: linear factors, non-linear factors, repeating linear factors... All of it. If you're new to partial fractions, you might want to review the other two partial fractions videos below, but if you've seen them before this video should cover everything you need for calculus.
Review from Pre-Calc:
Partial Fractions with "Non-Repeated Linear Factors"
That's a mouthful, no? This is the "easier" type of partial fraction decomposition problem where the denominator can be factored completely into stuff where there aren't any x2's -- or any other exponents -- anywhere in the denominator. I highly recommend you practice these before doing the next video.
Partial Fractions: Repeat & Non-Linear Factors
These are the harder decomposition with exponents in the denominator. Not so much harder, just more rules to remember and/or not screw up. Instead of just "A" and "B" in the numerators, you'll end up with stuff like "Ax+B", except when you don't. Makes sense, right?
If you do not have an account, you should get one, because it is awesome! You can save a playlist for each test or each chapter, and save your "greatest hits" into a "watch right before the final" list (not that we recommend cramming, but when in Rome...)