Integration by Partial Fractions | Big Idea + First Example

Integration by Partial Fractions is a little algebraic trick that converts rational functions (polynomial over polynomial) into something we can integrate fairly easily. Indeed, this algebra is a bit like "undoing" a lowest common denominator. We make a particular guess of the form, and this sets up a system of linear equations you can solve.

In this first video, we're only going to focus on the case where the denominator can be factored as a product of nonrepeating linear factors. In the next video we will talk instead about irreducible quadratics, and repeated terms.

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This video was created by Dr. Trefor Bazett, an Assistant Professor, Educator at the University of Cincinnati. #calculus #math

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[SMNAviation]

Incredibly underrated video. Easy to follow, great graphics and amazing explanation. Thank you.

[abrahamsweetvoice]

I forgot how to integrate by parts. Your youtube channel was the first thing which came up to my mind. Guys like you and other math/science related youtube channels deserve to be known as Hero's more than anyone else in this planet. I watched all of your calculus 3 videos and also some of calculus 2 (about series). After each video I watch I wonder why professors don't teach/explain like this while everything is so intuitive and easy to understand. I learned/understood math more on youtube than going to my theory classes and returning back home without understanding anything at all. I even came to a time where I was about to give up everything, because of thinking how dumb I am. After discovering yours and 3b1b's youtube channel I started to think that there is a huge problem with the way the students are being taught in all around the world. Seriously, tho?? Why don't professors teach like this. It's not only me, almost every student has this problem. I read comments about people why youtube is helping them more than Uni courses . I really can't thank you enough for all you did for me. I really don't know why you have not the views you deserve, but no doubt you and 3b1b deserve a noble price for math. One day if I graduate, I'm gonna look for you and give you 100 times the things back, you gave me during my college years.

[cajintexas]

Great video. I wanted to know, "Why partial fractions?" And your explanation simply answered that question.

[Looney_Lu]

Thank you! My professor is great but sometimes I need to take it in slower and see it piece by piece. Great visuals help.

[khayalethumakosi]

This is absolutely beautiful!! Math is FUNdeMENTAL (fun on the mental)

[duckymomo]

While integrating partial fractions is easy, decomposing it is annoying

Arguably it’s worth the hard work lol

[amanjadnan]

Thanks after 3 day I have an exam in this subject 😊

[mohammadghani]

is there any idea for the integration of 1/(x^m(1-x^n)) for m>0, n>0?

[duckymomo]

Is Gauss-Jordan elimination the best way to solve systems of linear equations?

[scribble]

andrew dismukes with a beard is prepping me for my exam