In this video I go over an introduction on the method of partial fractions for integrating rational functions. Basically rational functions can be simplified by breaking them down to partial fractions using partial fraction decomposition which in turn greatly simplify the integration process. For an in depth look into partial fraction decomposition make sure to watch my earlier videos shown in the links below.
Watch Video On:
- DTube: https://d.tube/#!/v/mes/wd1l29h8fta
- BitChute: https://www.bitchute.com/video/XTSzsvCSKiJX/
- YouTube: https://youtu.be/r07NnKf76og
Download Video Notes: http://1drv.ms/1ADF9by
View Video Notes Below!
Reuse of My Videos:
- Feel free to make use of / re-upload / monetize my videos as long as you provide a link to the original video.
Fight Back Against Censorship:
- Bookmark sites/channels/accounts and check periodically
- Remember to always archive website pages in case they get deleted/changed.
Join my private Discord Chat Room: https://mes.fm/chatroom
Check out my Reddit and Voat Math Forums:
Buy "Where Did The Towers Go?" by Dr. Judy Wood: https://mes.fm/judywoodbook
Follow My #FreeEnergy Video Series: https://mes.fm/freeenergy-playlist
Watch my #AntiGravity Video Series: https://steemit.com/antigravity/@mes/series
- See Part 6 for my Self Appointed PhD and #MESDuality Breakthrough Concept!
NOTE #1: If you don't have time to watch this whole video:
- Skip to the end for Summary and Conclusions (If Available)
- Play this video at a faster speed.
-- TOP SECRET LIFE HACK: Your brain gets used to faster speed. (#Try2xSpeed)
-- Try 4X+ Speed by Browser Extensions or Modifying Source Code.
-- Browser Extension Recommendation: https://mes.fm/videospeed-extension
-- See my tutorial to learn more: https://steemit.com/video/@mes/play-videos-at-faster-or-slower-speeds-on-any-website
- Download and Read Notes.
- Read notes on Steemit #GetOnSteem
- Watch the video in parts.
NOTE #2: If video volume is too low at any part of the video:
- Download this Browser Extension Recommendation: https://mes.fm/volume-extension
Integration of Rational Functions by Partial Fractions
One method of integrating rational functions (which are simply ratios of polynomials) is by expressing them as a sum of simpler functions, called partial fractions, that we already know how to integrate. To illustrate the method consider the following:
Now we reverse the procedure we can see how to integrate the function of the right side of the equation:
To see how the method of partial fractions works in general, let's consider a rational function:
where P and Q are polynomials.
It's possible to express f as a sum of simpler fractions provided that the degree of P is less than the degree of Q. Such a rational function is called proper. Recall that if:
where an ≠ 0, then the degree of P is n and we write deg(P) = n.
If f is improper, that is, deg(P) ≥ deg(Q), then we must take the preliminary step of dividing Q into P (by long division) until a remainder R(x) is obtained such that deg(R) < deg(Q). The division statement is:
where S and R are also polynomials.
The partial fractions will be solved using the methods in my earlier videos on partial fraction decomposition.