Improper integrals discontinuous integrand

SMALL MISTAKE at 17:34 - The antiderivative should be x - 2 +2ln|x-2| + C; I forgot to transfer the coefficient 2 when I finished the u-substitution! Even with the coefficient 2 missing, the end result of the question is still the same, the integral diverges to negative infinity. Shout out to chalumba ngalu for catching the mistake!
In this video, I go through 4 examples showing how to evaluate improper integrals with a discontinuous integrand. I show cases where the integral converges and diverges. Also, I carefully explain the concept behind this particular integral so that it is easier to set up the correct expression to evaluate.
If you found this video to be helpful, please LIKE and SUBSCRIBE. If you have any requests, leave the topic you want me to cover in the COMMENT section. Thanks for watching!

[@raed_ksa9449]

holy shit! I was browsing vids to learn how to do this crap then solve my homework but u just solved my homework! gonna cram this subject I guess

[@vinteachesmath]

I am glad this video helped!

[@alertbanda]

You're a genius kingman!!..Well cooked

[@vinteachesmath]

I appreciate the comment! I hope your end of year exams go well!

[@youngteacher3644]

Good 👍

[@vinteachesmath]

Thanks!

[@johnanam7802]

This is great

[@vinteachesmath]

I am glad the video was helpful!

[@tsheporaganya6677]

Your the best

[@vinteachesmath]

Thanks! I hope calculus is going well.

[@crazyjester993]

You could have used the integration of partial fraction here why didn't you use it 16:30 Don't forget negative number

[@vinteachesmath]

That is an alternate approach, definitely easier than u sub. Rewrite the numerator x as x - 2 + 2 then split the fraction into two fractions... I am planning on remaking some of my calculus videos. I mentioned that there was transcription error at 17:34, so I think I will do an all inclusive improper integral video. Thanks for the comment!

[@dpmike32819]

You made a mistake around the 21:18 mark..you forgot the 2 in front of the ln

[@vinteachesmath]

I realized it after the video and mentioned the mistake in the video description. This video took forever to make, I was so let down that I made that one transcription error! Great attention to detail that you noticed this!