integration by partial fractions with an irreducible quadratic factor

Learn how to do this integral of a rational function by using partial fraction decomposition. This integration has a cubic denominator and we will see how to factor it to get a linear factor and an irreducible quadratic factor.

For more calculus tutorials, check out my new channel @bprpcalculusbasics

[uncagedstudios]

I got a perfect score on my first Calculus II exam thanks to you. I think I owe you my tuition now.

[aurithrabarua]

Rather than traditional integration techniques, Partial Fraction Factorization was the main principle regarding this very integral..
Thanks for presenting to us!!
😊😊😊

[christianrodriguez]

bprp, I started watching your videos back in 2016 when I was first taking Calculus 2. Now in 2019, I am an LA for a Calc 2 class myself and I use your videos for inspiration to help my students study and give them a little challenge here and there ;D I’ll definitely ask them this question tomorrow since they have just finished going over partial fraction decomp. Thank you so much for the past few years of tricky math content, and for future content to come :D

[DanielGonzalezL]

Hey, they never taught me that way to factor things out you did at the start of the video! Thanks!

[chinesecabbagefarmer]

Thanks for this upload! Partial fractions can be confusing, and you made it simple.
Hope all is well.

[Steve_]

This is the only channel on YT where I can always find the most interesting and complicated things related to Calculus. Most of the videos are useless since extremely easy and every student preparing Calc 1 or 2 already knows all that stuff.

[wuyqrbt]

Thank you dear teacher, b🖋️Pr🖍️P ❤️

[yoavshati]

Instead of doing the long process of partial fractions, you could have notices the +8, which is a multiple of +4, and the -3x, which is a multiple of -3. Then ou can quickly check to see if it works out with the x^2 term, which it does here, and you can seperate the fractions

[gourabghosh]

Two random points are selected inside a cube of 1 unit. What is the average distance of the two points?pls solve this

[mdnazmussakib]

So brother, I am from Bangladesh. your videos regarding mathematics are interesting. It will be great if you answer my questions.
1. What is the formula of median and why so!?
2. What is the formula of mode and why so!?
It could be in mathematics and also statistics.

[fatimafrancodesilva]

Thank you so much!! You are the best, love the vibe!!

[holyshit]

We can guess how to express integrand as a sum

and then in first integral we can sustitute u=x^3-3x^2+4x-12
in the second integral numerator cancel with denominator and we can substitute v = x^2+4

[ameersahi]

Good job.. how the value of A=2 ?why x=3?
Thanx.

[johnpatrickobra]

I am an electrical engineering student, thank you very much for sharing this method! MABUHAY!

from Philippines.

[VaradMahashabde]

NICE
I was trying to factorise the numerator😅

Do you have a dedicated partial fractions video?

[ligleaper]

Very valuable technique for advanced level math, i.e. Differential Equations.

[yrret]

just wondering, if you use the cover up method on x^2+4 with x=2i will it work?

[pablofueros]

Thanks so much for this video, I needed it!!!

[Gab]

After finding A, to get B you can multiply by X and compute the limit to +∞, you easily get 3 = A + B --> B = 1. To get C just X = 0.
Sorry if this has already been said in the comments.

[krishnarajasagar]

Great job, mate!! Your presentation is very cool.:):)