Integration by Partial Fractions: Example 9: Rationalizing Substitutions

in mathematics •  2 months ago  (edited)

In this video I go over another example on integrating rational functions using partial fractions and this time show how sometimes even if the function we are integrating is a non-rational function we may be able to rationalize it or make it into a rational function using an appropriate substitution and thus be able to use partial fractions. The example I cover in this video is the integral of the function sqrt(x+4)/x and show how we can use the substitution u = sqrt(x+4) to transform the non-rational function into a rational function. This is a very useful technique to have when integrating non-rational functions so make sure to watch this video!


Watch Video On:

Download Video Notes: http://1drv.ms/1O29Qsp


View Video Notes Below!


Download These Notes: Link is in Video Description.
View These Notes as an Article: https://steemit.com/@mes
Subscribe via Email: http://mes.fm/subscribe
Donate! :) https://mes.fm/donate

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!

Follow My #MESExperiments Video Series: https://steemit.com/mesexperiments/@mes/list


NOTE #1: If you don't have time to watch this whole video:

NOTE #2: If video volume is too low at any part of the video:


Integration of Rational Functions by Partial Fractions: Example 9: Rationalizing Substitutions

Integration by Partial Fractions Example 9.jpeg

Some nonrational functions can be changed into rational functions by appropriate substitutions.

In particular, when the integrand contains an expression of the form:

Then the following substitution may be effective:

Example:

Solution:

Authors get paid when people like you upvote their post.
If you enjoyed what you read here, create your account today and start earning FREE STEEM!