life changing integration by parts trick

Let’s learn a life-changing integration by parts trick. Once you learn this integration technique for you calculus 2 class, many integrals will be much easier. The trick here is to choose a clever antiderivative with a smart constant.

0:00 Intro
0:15 Integral x arctan x
2:20 Integral ln x+2
3:30 Integral arctan square root x+1

[ThJakester]

This technique is absolutely crazy. I feel like I now have the confidence to ask my boss for a raise and find a beautiful wife to marry. Thanks, Dr. Peyam.

[blackpenredpen]

This is actually really cool 😆
Glad I actually watched it haha

[nonentity]

Now the +C is actually useful. Great video

[DrTrefor]

How did I not know this. My life is changed.

[gamingroom]

3:11 “Isnt that nice!” Nice ? NICEEE ??? SIR THAT IS STRAIGHT AMAZING my life is never the same after this

[liamloveslunch]

"Arent you glad I found my video? 😁" Yes! So happy!

Glad to see you so happy about math too :)

[sharpnova]

I've taught this method to my students for years and it's always made them much better at integrating in general

[krischalkhanal]

I remember asking teacher, "can we add a constant to *inner integration* in the formula of integration by parts?"
He told me, "only a single +c can appear in a single integration", which feels so stupid to me now.

I am so glad I found this video. Kudos to you Dr. Peyam.

[floydmaseda]

Thought the title was click bait.

It was NOT click bait.

Life changing, indeed!

[sayantansaharoy]

I love his attitude, man knows math and is happy about teaching it. I wish all my teachers were like him.

[aaronpahler]

As a physic student I can say, this is really lifechnaging, hours of pain will be joy instead. Thanks 🙏🏼

[MrTomas]

Wow, such a simple idea that's hidden in plain sight! Just in time for my calculus test this week.

[emoneyuz]

blessed to have him as my differential equations professor, couldn’t be luckier

[kobethebeefinmathworld]

The fact is (even if we just think up to calculus level): whenever we do antiderivates, 99% of the time we forget the "+C", and this "+C" is the reason why we can end up with different answers depending on how we choose. Moreover, this also shows that the operation of antiderivate is not even a function as we can pick anything in the codomain for C as we want. So as long as the "number" that we "need" belongs to the codomain we can add it freely.

[MuPrimeMath]

How have I never seen this before? This is amazing!

[skylardeslypere]

To be fair, the integral of x²/(1+x²) is relatively easy because that's just (1+x²)/(1+x²) - 1/(x²+1) which gives x - arctanx
But nonetheless, this is a really useful trick I've never thought about. Nice video

[violintegral]

This is one of the reasons why integration by parts is my favorite (and in my opinion, the most powerful) integration technique. Here's a really great (and difficult) integral for anyone interested: ∫√(1+x+x²)/(1+x)dx. Keep IBP in mind!

[vrtxactivewear]

I've learnt the +1 -1 trick. on integration but this takes it to a new level - can't thank you enough!

[stevehof]

This blew my mind! So fascinating. I guess that's why in my courses it usually says "find the most 'general' antiderivative."

[tomctutor]

Never thought of doing that, gonna call it the "Peyam Integration Method"
Something quite related of course is shifting the function,
so; ∫ f(x+c)dx = ∫ f(u)du letting u= x+c.
Ex: consider ∫ x/(x+1)dx 
➙ ∫ (u-1)/u du with u= x+1, gives ∫ (1-1/u)du = u- lnu = (x+1)-ln(x+1)+const.
Be careful though to change limits in definite form,
so ∫ f(x+c)dx between x=a to b ➙ ∫ f(u)du between a+c to b+c