Integration by Partial Fractions | Big Idea + First Example

[@SMNAviation]

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

[@abrahamsweetvoice7687]

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.

[@cajintexas7751]

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.

[@khayalethumakosi6678]

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

[@mohammadghani1379]

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

[@duckymomo7935]

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

[@duckymomo7935]

Trefor Bazett Ohh I can’t wait for that linear algebra course

[@carultch]

@@duckymomo7935 Depends on what you want to solve for. When you want all of the solutions, Gauss-Jordan elimination is the most computationally efficient method, and has the advantage. When you just want one of the solutions, Cramer's rule has the advantage. Cramer's rule also has the advantage when solving one by hand, that isn't immediately obvious for how to proceed with Gauss-Jordan elimination. With GJE, you have to determine what the row operations are, in order to make it work. With Cramer's rule, you just plug and chug determinants.

[@amanjadnan8466]

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

[@duckymomo7935]

While integrating partial fractions is easy, decomposing it is annoying Arguably it’s worth the hard work lol

[@carultch]

One trick that makes it super easy, is Heaviside Cover-up. For linear terms, and the largest power of repeated terms, simply find the x-intercept that makes each denominator factor equal to zero. Then cover up the denominator of zero, and evaluate the fraction. That becomes your answer for that particular term's numerator. This allows you to eliminate a lot of the excess algebra. I like to organize my partial fractions such that the Heaviside cover-up terms come first, and get priority to be A and B, and if applicable, other early letters. For the other terms, a trick that simplifies your algebra, is to look for special case values of x, that are either easy to evaluate, or that eliminates one of your unknowns from your equation. Like 1, 0, and -1. We can't use x-values that we already used for Heaviside cover-up, so if those are spoken-for, we'd have to look elsewhere.

[@Bruce-ip2it]

thank you so much prof Dr Trefor

[@rekhapathak6752]

Thanks a lot sir

[@danbilzerian5918]

Finally understood tqqqq

[@yasminkhalifa7581]

Thank you so much

[@user-uc7tw1kg8i]

this shii lowkey make sense twin

[@scribble8116]

andrew dismukes with a beard is prepping me for my exam