A great integral calculus review in one problem!!

[@IoT_]

Now we need to check the result by differentiation

[@noahtaul]

10:55 You need an extra 1/2 on the front of these next two integrals because you removed the parentheses

[@red0guy]

yeah

[@megauser8512]

Yes, he forgot that.

[@Aditya-jv9mp]

Yeah left me confused a little bit

[@duckymomo7935]

So it should be 1/4 and 3/4 in front of later integrals

[@WielkiKaleson]

Very true, but... Would that make the final result less nasty?

[@robshaw2639]

I just realized that not only is Micheal Penn an extraordinary instructor, but he has great Mathematical agility over a diverse set of subfields... i predict Micheal will discover why the Monster group is what it is, or will make some completely new groundbreaking contribution to Mathematics in his lifetime. I just hope that i live to see it....

[@lexinwonderland5741]

the guy studies VOAs and other things that modern physics is still looking for, I wouldn't be surprised if he or more likely one of his students made a fantastic discovery about that sort of thing. but me too, i'll be thrilled to watch his career!

[@johnnath4137]

More simply: 1 = A(1 - u + u²) + (Bu + C)(1 + u): setting u = -1 → 1 = 3A → A = 1/3; setting u = 0 → 1 = 1/3 + C → C = 2/3; equating coefficients of u² → 0 = 1/3 + B → B = -1/3.

[@dujas2]

That substitution seems like it comes out of left field, but it can be done in 3 steps. First, x=arctan t to remove the trig, t=v^3 to get rid of the cube root and set up partial fractions, then finally u=v^2 to simplify.

[@vittorio1159]

Now check the answer by differentiation ...by definition

[@anshumanagrawal346]

Lol

[@JCCyC]

(Insert meme of Mojo Jojo and Him shedding tears of joy)

[@hsjkdsgd]

He carried all the 3 integrals to the very end when he could've easily annihilated the two of them (1/1+u & 1/t) just after partial fraction decomposition. Great display of patience!

[@tylerm442]

All it's missing is integration by parts lol

[@beoptimistic5853]

kzbin.info/www/bejne/joKsk6FobMmCoKc 💐👍

[@Verifyourage]

At 11:00 multiply the numerator by (2) = 2u-4 then multiply by 1/2 outside the integral to get 1/4 apply the sum rule 2u-1/ u^2-u+1 minus 3/u^2-u+1

[@diniaadil6154]

u = tanx^(1/3) does help getting to a rational function but with u^6 in the denominator which can be simplified further with a u² substitution. Overall it's the same as using your method but it's much more intuitive to simplify step by step rather than comming up with an overly complicated substitution.

[@schrodingerbracat2927]

for partial fraction decomposition, here is a trick I discovered:- by the "cover-up rule", you can get 1 / 3(u+1) easily. then you COMPUTE 1 / (u+1)(u²-u+1) - 1 / 3(u+1) ALGEBRAICALLY to get (2-U) / 3(u²-u+1). So there is no need to solve for A, B, C.

[@lucashoffses9019]

Oh my god He never noticed that he forgot to distribute 1/2 to the second integral.

[@bakul1978]

Yes

[@DeanCalhoun]

I think watching your videos is working because I was able to intuitively guess pretty much every step along the way. What a great integral. Thank you so much for your videos!

[@frozenmoon998]

Hardest integral on KZbin: Prof. Penn: *Hold my beer*

[@Fun_maths]

Hold my chalk, wait don't hold it I need it to write on the board

[@mcbeaulieu]

Even your "2u" has music to it. That's perfection right there 🙏

[@muskyoxes]

The lesson i got out of this is that it's somehow possible to do a ton of work on an integral without ever using integration by parts

[@FatihKarakurt]

combine the first two ln functions to get back the (1+u^3) in the argument which will simplify the result a bit.

[@FatihKarakurt]

@@angelmendez-rivera351 Yeah, it seems I made a sign mistake as well.

[@goodplacetostop2973]

19:22 Loading 94.9%...

[@integralboi2900]

I just realized the loading percent is Michael’s subscribers…

[@holyshit922]

If we play with substitutions we can get following u=sqrt(3)(1-(tan(x))^(2/3))/(1+(tan(x))^(2/3))

[@The1RandomFool]

As an alternative, you can do a substitution u^3 = cot x. After simplification, you can substitute again with u^2 = v the rest is similar to the video.

[@leif1075]

Whybwoukd anyone pick the isub he did right..isn't it random out of nowhere

[@FoxtwoPC]

I always always forgot to add a constant to indefinite integrals...my exam answers were always pages of triple checked algebra that resulted in -2pts for forgetting the +C

[@roberttelarket4934]

Michael Penn the "energizing bunny" cranking one great math video after another!

[@berzerksharma]

I guess u missed a 1/2 while decomposing the integrals

[@megauser8512]

Yes, he did!

[@andrewdsotomayor]

Yeah, I noticed that as well

[@SlidellRobotics]

Yes. At 11:44 he needs parentheses around all but the leading 1/2.

[@bakul1978]

@@SlidellRobotics Yes

[@TheOneThreeSeven]

12:32 dt ear muffs !!!!! can we get that in the merch store please =)

[@yousifkhalil9655]

only u sub, trig identities, simplification, partial fractions, cubic factorization, completing square, add & subtract a quantity, dismantle integral and t sub in a u sub! i thought there were gonna be a trig sub, by parts, long division, multiply by conjugate, multiply numerator and denominator by another function (as with secx) and a use of definite integration properties with infinite intervals and discontinuous integrands as well

[@JvnKnght]

"That's kind of a bummer" at the end when subbing back for x. Had me laughing my ass off

[@rafael7696]

Great video, as always

[@Pauldyke]

Finally, some fun stuff!!!

[@get2113]

His integration tricks are great

[@sophieward7225]

I like ya cut, P! *slaps down integral of 1/cbrt(tanx)*

[@Chalisque]

KZbin displays suggested videos and your channel logo at the end (20s from the end of the video), which obscure the blackboard. Perhaps when you edit you can squeeze an extra 20s at the end after your 'good place to stop'.

[@AmrishKelkar]

Try the integral of the reciprocal of the fifth root of tan x!!

[@omachiyogi]

3:47 I usually just use the positive square root too. However, why can we just do this instead of considering +-sqrt(u)?

[@musatebi486]

I cant focus on the problem, I want to press play button on his shirt but it does not work.

[@megauser8512]

LOL!

[@viktor-kolyadenko]

In 6^20 we can: 1. Easy give A. 2. Easy give Bu + C.

[@antarctican5284]

I started by u subbing the whole thing

[@sankimalu]

I like the multitasking: integrating household chores with educating the masses.

[@EyadAmmari]

Just a note that you forgot to carry a 1/2 when you were breaking up the quadratic part.

[@michaelfisher9053]

The constant multiplying the arctan term should be 1/2 sqrt(3). The constant multiplying the ln(tan tan) term should be -1/4. Otherwise he nailed it.

[@dougjohnson4917]

Why not make it an arc tan function at 4:24?

[@CTJ2619]

i lik it when you explin PFDs

[@RobertMOdell]

shouldn't the natural logs at the end be surrounded by absolute value ?

[@CM63_France]

Hi, Got the missing 1/2 as well, or the missing parenthesis. Why Penn whith 2 n's? For better SEO ? :D For fun: 3 "ok, great", including 1 "ok, great, so now let's go ahead and", 1 "I'll go ahead and", 1 "but let's go ahead and",

[@davcaslop]

17:25 why didn't he use absolute value?

[@jack-jt2lm]

very nice teacher

[@qillerdaemon9331]

Great! Wonderful! Except it's the final, there are 10 problems almost identical to this one, I have an hour to complete the exam. And I've just spent almost 20 minutes solving one of them. :(

[@abraarmasud9194]

If this is an informal exam, maybe we can help you out. Share the question?

[@qillerdaemon9331]

@@abraarmasud9194 It was just a joke, buddy. :)

[@f5673-t1h]

Is Michael Penn short for Michael Pennsylvania?

[@Scaw]

That suggests that Billy Connecticut fought Joe Louisiana twice for the heavyweight boxing championship of the world in the 1940's.

[@johnnath4137]

I looked him up in Wikipedia and was puzzled about the strange stories I was reading about his politicking and other shenanigans, and nothing about his maths. At long last I realised that I was reading about one Michael Pence (who is he anyway?) whereas I should have been looking up Michael Penn.

[@duckymomo7935]

He’s from VA www.michael-penn.net/about-me

[@ArgumentumAdHominem]

This solution only works if tan(x)>0. What happens when this is not the case

[@avalanche2022]

really good

[@mbarkaitkerrou6734]

Monsieur Michael Penne est est-ce que vous pouvez trouver cette primitive sans utiliser le changement de variable et mercis infiniment.

[@Paul_Hanson]

non

[@jimcameron6803]

I was going to watch this, but I went and watched blackpenredpen's video on the same integral instead. It was a classic KZbin-substitution.

[@lexinwonderland5741]

Is there any way to reduce functions of the form arctan(k*tan(x))?

[@수하긴]

15:23 I never expected that M'kay really exists

[@samegawa_sharkskin]

i thought this would be like bprp's integral video of cbrt(tan(x)) and got scared but it's really not as bad as that

[@nontth5355]

I just finish my calculus exam and did 1+2=6 and 1-(-1)=3 and lost 2 points. Is there any cure for stupidity? I really need it lol

[@anilsharma-ev2my]

Taking square root of integration gives us what ?

[@matematicaconjuliocesar6366]

Excelente

[@sushantyadav7806]

Where does this arc word came..not understood

[@vaxjoaberg9452]

Arctangent (arctan) is the inverse of the tangent function. if tan(x) = y, then arctan(y) = x

[@FaerieDragonZook]

Looks like you're missing a factor of 1/2 at the 11 min mark

[@user-A168]

Good

[@jabunapg1387]

I don't understand what he does there on 11:00 ???

[@Ni999]

u - 2 ½(2u - 1 - 3) ½(2u - 1) - 3/2 He got ½(2u - 1) + 3/2 from -∫(a-b) = -∫a + ∫b. He still missed multiplying through by the ½ outside of the original parens.

[@leif1075]

WHY ON EARTH would anyone do that substitution of u equals tan^2/3 I don't know why anyone would think of that..

[@123ucr]

This would be a Calculus 2 final problem.

[@jamirimaj6880]

Folks, remember: This is the EASY way of doing this. 😑

[@josephcollar5987]

What's the damn point....🙄😒

[@atrakchi2]

vielen Dank es war Großartig Danke nochmal

[@robshaw2639]

After watching this channel for several months now, im really getting a gut feeling that Micheal is the next John Conway...

[@ameerunbegum7525]

*NOICE*

[@AstroB7]

Wrong answer Mike

[@mza3764]

someone is playing fp shooter in the background

[@jaimeenriquediazdiaz2341]

Oooh good heair cut, yes perfect and KZbin lesson mate is ver good so much very much like

[@juanmolinas]

wow, what a stunt, I wouldn't have seen it ...

[@klementhajrullaj1222]

At the end your hairs! Peace, relax and harmony! ...

[@Tiqerboy]

I see your video is 20 minutes, presumably to solve this integral. Wow, can't be easy, especially since I forget most of what I learned way back then. It's not everyday you have to find the antiderivative of trig functions. God, is the answer ever messy! I was watching the MIT Integration Bee. They are only given 4 minutes to solve problems with that.

[@polsker]

Wrong answer tho

[@duckymomo7935]

The answer is mostly right except for the constants Sqrt(3)/2 and 1/4 front of log(tan^(4/3)...) which is where he missed the 1/2

[@jackthisout9480]

A tricky integral he says. I'd say it's pretty triggy.

[@duckymomo7935]

Integral Sqrt(tanx) is a nightmare

[@Ni999]

Not this way - _Integral of sqrt(tan(x)) ... Impressive method...calculus concepts_ kzbin.info/www/bejne/moWbk2utds-Hga8 Minor typo in it, I mentioned in the comments.

[@neilg2256]

太复杂了，草稿纸要写三张

[@agrajyadav2951]

tedious

[@impk100]

It is wrong

[@fonzi102]

absolute value missed

[@isaacdeutsch2538]

oh my g-d he forgot the ½ oh my g-d he can't hear us 😨

[@anasuit1111]

うーん、まぁ難しくない

[@mashtonish]

Sorry, I wish I could watch for more than 5 minutes before getting bored :[