Calculus II: Partial fractions

In this video, we discuss the idea of what partial fractions are and how we can use partial fraction decomposition to evaluate integrals involving rational expressions.

00:00 - Introduction
00:16 - Introduction to partial fractions.
04:20 - Table of partial fraction decompositions
08:47 - Example 1
16:35 - Example 2
21:52 - Example 3
32:05 - Example 4
46:02 - Example 5

[emmavandeventer]

Thanks for the video Cloudy! Appreciate it

[MathforThought]

At the end of example 1 the answer should be 4ln(x-3)-ln(x+2)+C. I made a minor typo.

In example 2, the 5/2 should be a 5/6 for the final answer.

[jasonmantri]

for example 3, why is the integral 2/x^2+3 not 2ln(x^2+3)? Can we express it like that or do we need to use the arctan method?

[charlottehuber]

Hi, Question: In Example 2, in the final answer why isn't it 5/6 instead of 5/2. I am wondering since when you take the derivative of a log you multiply by the derivative of the argument, is this incorrect?

[ayusharies]

first example answer should be 4ln(x-3)-ln(x+2)+C right?

[eyadmostafa]

@33:50 (example 4), should it (A+B+C)(x) instead of (A+B-C)(x)?