Calculus 2 Lecture 7.1: Integration By Parts

[@lordosmosisx8653]

This is exactly how calculus professors should be. They shouldn't be as dickish as they are just because a student doesn't understand the material. Some of us aren't configured to just "get it." Professor Leonard is excellent. He breaks things down and explains along the way. You can tell he cares about his students, and has fun along the way, seen in his comic relief. The fact that he is able to make students smile in a class as difficult as this shows a lot. You are a good person. Thank you for all your help!

[@RodneyFisk]

Yeah, I was lucky to have 3 great Calculus teachers in college, like this guy. I had one bad one, and failed Calc I the first time. Took it again during the summer and made an A.

[@shreksburgers]

@@sebastiansebastian5270 bruh i got the same teacher. i guess this guy is gonna be my replacement prof.

[@instaminox]

you should teach teachers how to teach

[@norahnoman8661]

+ihonestytruthful exaxtly

[@Tuffadandem]

+ihonestytruthful Absolutely!!!

[@sonnywu100]

+ihonestytruthful yeah, same lecture and textbook, i get him instantly while i didnt get sht in my lecture.

[@Love001u]

+ihonestytruthful agree some of the teacher are bad, they just base it out of the book which is not helpful and they write more words than examples and they go everywhere and are not organized -.-

[@kai_onlineaaa]

+Veronica mesinita ^^^^

[@gotosleep1816]

Professor Leonard- "I need to make sure that you understand" My Professor-" If you don't understand go home and practice"

[@Brandonmx75]

my professor- "if you don't know it, this class is taught every spring". A literal quote from one of my chemical engineering professors

[@Peter_1986]

My professor: "Ah well I will just do this lecture thing I guess, and I don't really give a crap about the students' understanding".

[@undefined.infinity3106]

literally, my course teachers are said the same thing

[@hawtpotato90210]

@@Brandonmx75 Please tell me you made it

[@DeeRandhawa]

Prof. Leonard: "Show of hands if you are ok with that one" Me: Actually raising my hand with a smile on my face :D

[@salmauthmaan4954]

lol!! thought was the only one

[@jonathanswinsburg7716]

every time

[@Shadowbrothe]

I do it all the time! even though I'm sitting by myself with a headset on, I raise my hand!

[@hamzikC3]

😂The same here

[@darthboganis1356]

Before, you made it fit the integration tables. IBP is the product rule for Integrals. 0:00 Deriving the IBP formula 1:00 Why Integration by Parts? 8:00 Choosing u and dv w/ example 10:30 Example 18:00 Process: Is it in the table(can you rewrite it)? Can you substitute? Integration by Parts? > If it's not solvable.. consider IBP a second time on right side of plus sign, or substitution Example 28:30 [Substitution or IBP?] > 36:30 IBP twice More examples/philosophy of IBP 41:50 What to do when IBP runs on a cycle? 52:00 add the repeating component (the component you are trying to solve for from the beginning shows up on the RHS) to both sides. This works because you have an equation effectively. Example 58:40 integral of ln (x) w/bounds [1 to e] Example 1:06:30 If nothing is working, break into components that you know you can integrate > insert an identity to make it easier to solve 1:11:30 > sec^3(x) integral 1:16:00 > this problem also took advantage of repeating integrals which can be cancelled out Reduction formula 1:29:15 Reminder on IBP philosophy 1:32:30 > using an identity 1:39:50 > splitting up the integrals, moving repeat component to LHS 1:43:00 > the official reduction formula for sin 1:47:15

[@blakehill625]

One of the ways my calc 2 teacher said to help remember the integration by parts formula is "ultra-violet voo doo" UV - Int(vdu)

[@alan912-qi1ew]

What a disgusting teacher

[@adame2037]

a little tip: If you ever want to know what to set U equal to in the equation use LIPET. L is log functions (ln), I is inverse trig (sin^-1(x)) , P is polynomials (x, x^2, etc), E is exponential (e^x), T is trigonmic functions (sin, cos, etc) Do this in order, if you have int(xlnx)dx for instance, you set U=LN because it comes before polynomials in the pneumonic This will work in any situation using integration by parts!

[@adame2037]

Trevor Yilk a polynomial doesn't need to be made up of two or more monomials to be considered a polynomial genius...

[@champbailey88]

+Adam Elmallah how come in the example where it is e^xsin(2x)dx he uses sin(2x) as u?

[@chiragpatel849]

+Adam Elmallah Thank you, this saves so much time on the test!

[@fatimazaghab4262]

Actually Its LIPTE

[@adame2037]

Fatoom Zaghab no lipet works perfectly fine

[@riaregi9029]

I don't even know why I bother going to my Calc class because I learn more from sitting at home and watching these lectures. Thank you, Professor Leonard! Heads up to anyone reading the comments, but an easy way to pick your U is to follow LIATE (log, inverse trig functions, algebraic terms, trig, and exponential). It works most of the time so keep that in mind.

[@cilva7able]

shut up

[@huanglinwan7075]

so rude

[@Shadowbrothe]

Professor Leonard, I hope you get to read this, I started college 20 years ago, had a son in my first year, "took a break" to enter the work force to provide for my family. While I have done very well for myself without completing college, becoming a widely sought after industry leader in my profession, I decided it was time to continue my education. Fast forward 20 years I am working full time in a pretty demanding industry with quite a lot of responsibility and I'm trying to continue my education. Disregarding what I've spent in tuition for formal education, you are the reason I got an A+ in Calculus 1 (don't forget I've been 20 years out of school and only remembered basic college algebra), and now you are the reason I'm understanding Calculus 2. I can't express enough how amazing you are as a professor, and I will be contributing your Patreon. I've spent weeks and weeks trying to understand Cal1/2 from the book, and course material, and visiting a few of your lectures makes everything click into place. I can't contribute enough to your Patreon to let you know just how much you have done for me. I completed Cal1 with an A+ in 5 weeks after not doing advanced math for 20 years, if that does not speak to your ability as a Professor I don't know what can. I could only wish I had you as a Professor in person... Thank you!

[@MashrufKabir]

" Whatever you see, it goes for your V. " - Professor Leonard

[@tychothorpe4515]

It is an honor being taught Calculus by Clark Kent...

[@SJ23982398]

+Tycho Thorpe The derivative of Superman

[@tychothorpe4515]

is Batman

[@Raphaelshreds]

+Sjaak Trekhaak Or it could be Superman just as the derivative of e^x is e^x. The derivative of Superman is Superman!

[@michaelempeigne3519]

The derivative of superman is kryptonite

[@jacobsolanki6216]

If we consider Superman's body to be a curve, wouldn't the integral of Superman be Clark Kent, because the integral is the area underneath a curve and Clark Kent is who Superman is in on the inside #MindBlown

[@victorotieno1390]

anyone who hates maths will change his attitude after watching your video...you are such a wonderful instructor....kudos

[@DanT-iu6oc]

was having a bad day struggling with Math and Prof Leonard completely cleared up misunderstandings. This man is a NATIONAL HERO.

[@dinamohammednur7928]

Correction* International hero 😊

[@seeziwei7511]

international hero

[@AnnyMay6]

Let me get this straight. So the alphabet has 26 letters, why in the world did the math geniuses had to choose the two that look the same????????

[@AnnyMay6]

***** so does J and K, my point is that there are so many letters that they could've used, yet they chose the two that look almost the same.

[@AnnyMay6]

***** anyway I don't think I'm going to be using this method again I my life since I finished calculus 2 and differential equations.

[@AnnyMay6]

***** calculus 3 is under the name of differential equations in my university

[@zekeriyakayamathclass5251]

as additional u is also used for substitution

[@Peter_1986]

I always use A and B myself.

[@merritt2014]

You can pinpoint the exact moment that Professor Leonard's soul died when his students told him integral ln(x) equals 1/x lmao.

[@CaulkMongler]

20:15

[@db7979]

Also 59:24

[@austinoquinn815]

same guy 😂

[@vishalkaranam]

hulk angry

[@Nico-ur2po]

who dey

[@FakeWonder]

If my whole class knew about this channel I'm pretty sure my professor would be without a job

[@mugdha1942]

All i've to say is he's a magician. Calc2 has never been better!Thanks prof

[@thebassofmontecristo]

Any Calc teacher would be hard pressed to come up with a clearer, simpler, better explanation than this one. This guy is a math rock star and has given me the hope of passing Calc2 with a high grade.

[@yuriorlov47]

Rafael Montecristo how did calc 2 end up for you?

[@thebassofmontecristo]

Evan Valek Might be hard to believe but l got perfect scores on all tests. Same with Calc3 and Differential Equations. I had to bust my butt practicing for hours and hours, but it was worth it.

[@yuriorlov47]

What Calc book were they teaching from? what is your career path?

[@thebassofmontecristo]

Evan Valek Larson 9th edition. But l just used it for the exercises. l used this channel's explanations instead of the book's.

[@thebassofmontecristo]

Evan Valek Aerospace Engineering.

[@dementedfairy7373]

You lectures have actually allowed me to watch your lecture in my room when I'm too depressed to go to class. I must thank you for this.

[@mastovlox]

For anyone else who's looking, Reduction Formula 1:29:40

[@missidontcare2121]

Omg, thank you! I came back from 7.3 to find it.

[@michaelsandink6940]

@Wesley RichardsonThis is a bit late, but it does not. It just needs to be greater than or equal to 2.

[@sakenmuratov7670]

God bless u mate

[@vikesboy00]

I can't say it with enough conviction, but YOU ROCK!!! There are EXPERTS who TRY to teach. There are TEACHERS who are not EXPERTS and then there are the type like professor Leonard: TEACHERS who are EXPERTS. Thank you!!

[@lorraine5800]

This is just about the luckiest class of Calc. II students... thank you so much Prof. Leonard for uploading this lecture & sharing the knowledge with others!!!

[@jamesgrey3320]

in france we don't have teachers looking like clark kent ! this man is sympatic and you understand that he's passionnate by teaching. the pupils have a great chance to have that king of teacher i follow his course because he makes math very clear ! merci professeur from france

[@redjar69]

This man got me through Calc 2 when my professors could not. Bless you Professor Leonard

[@laxel01]

LOL 6 YEARS LATER, STILL SUPERRR USEFUL! I had to take a break from my calc 2 online class especially during the pandemic! This is just what I needed

[@kobioreilly4753]

Two university calculus professors and one AP high school calc teacher have taught me integration by parts, and you did in the first 6 minutes of this video what none of them could in three years. I'm subscribed and staying that way!

[@kai_onlineaaa]

if I'm able to pass my calc 2 class i'll owe my life to you

[@kai_onlineaaa]

anko Mitarashi I did, but my professor was wack. His test were nonsense but these videos were be helpful. If i actually watched more of these I would have probably been able to get a better grade

[@wellbangok8959]

anko Mitarashi good luck in calc 2, my god was this class a nightmare. Calc 3 wasn't as bad but it depends on the professor, and Diff EQ is similar to calc 2.

[@IXXIrusty]

Did you pass Calc 1?

[@carlkpsplucky5554]

We’ll Bang, Ok? What profession did you go into with all this calc?

[@a_smile55]

@@wellbangok8959 How's live treating you now?

[@tonismith4214]

I'm in Calc 2 right now and I'm actually listening to his lectures instead of my professor's. Best explanations....way simpler. It's just amazing how teaching style can alter what a student understands.

[@lordosmosisx8653]

This man is saving my life.

[@DesertDwight]

This man won the genetic lottery.

[@giancarlodisalvo1784]

Or he just works hard? WTF kind of comment is that. You think he was just born knowing all this calculus?

[@GabeE3195]

@@giancarlodisalvo1784 I think they're referring to his appearance lol.

[@giancarlodisalvo1784]

@@GabeE3195 Pretty sure he works hard for that as well, though I missed that

[@GabeE3195]

@@giancarlodisalvo1784 Yeah he probably does lol

[@RayWalker-pythonic]

This professor provides the best explanations for calculus I've ever seen. He illuminates so many crucial points that I've just assumed from the repetition of solving problems. Osmosis, I guess. I've always known I'm integrating twice for "v", but no one ever explicitly stated it and sometimes that would trip me up because I'd wonder in the midst of solving a problem, "am I really supposed to be integrating twice? Does that work?" Same for just including the rest of the integration for v. Nice to have this kind of precision so I don't second guess myself.

[@georgesadler7830]

Professor Leonard, thank you for an outstanding explanation and detail analysis of Integration by Parts in Calculus Two. Integration By Parts is a powerful Technique of Integration in Calculus, however solving problems using this method can get really messy from start to finish. This is another great integration tool for all students in Science and Engineering. This is an error free video on KZbin.

[@RayZ842]

Thank you Prof.Leonard. I know that my comment might be trivial to you, but you mean so so much for me in Calculus class. You not only saved my Calc 2, you made me LOVE it. You make math become something I feel excited about and attracted to for the first time in my life. So a huge, huge thank you. Love your humor and teaching and everything. It's my luck to be your student.

[@muhammadsaminyasar7093]

An easy way to pick u is using "LIATE" L= Logarithm, I = inverse trigonometry, A = Algebra (normal x and stuff), T = trigonometry, E = exponential (e^x). Basically LIATE helps you determine what type of functions takes precedence when you need to pick u for integration by parts.

[@luckn.3371]

crazy helpful God bless

[@HenryBriskin]

I think your right

[@taeganmae8373]

It's honestly so sad to see that there are so many people trying to reach their goals and do well in school, and calculus seems to always just bring them down (myself included lol) for a number of reasons. The biggest reason I see so far is that students are absolutely failed by the system by being stuck with professors who do not know how to teach. I'm in Calculus 2 right now, and I was lucky enough to have really awesome professors for Precalculus and Calc 1, but it is the biggest struggle trying to succeed in a class with a professor who can't teach. I see lots of professors who are very smart, and knowledgeable enough to be teaching their subject, but they simply just are not able to teach it to other people. This guy, however, is a literal superhero for those of us who are unlucky and maybe don't have the best background in math or are stuck with a bad professor. It takes so much passion and effort to do this for other people who he doesn't even know, but it is GREATLY appreciated and gives all of us hope that we can succeed in such a difficult class. Professor Leonard, thank you for everything that you do to help students across the country.

[@marvelmanbatman77]

your students have no idea how much of a blessing you are

[@yoda101]

I'm not even taking calculus but he is such a good teacher I have been watching for 45 minutes.

[@syremusic_]

Absolute champ. One of the best ways for me to learn is to just have someone walk me through the damn thing a few times. Cheers Prof.

[@Robot_Chimp]

I miss the coughing kid in the calc 1 lectures, I hope he is doing well in life

[@sevranararis7704]

You're letting me retake Cal 2 before my actual Cal 2 class finishes, you are a great man, and you have my eternal gratitude.

[@TheFarmanimalfriend]

I'm going back over the Calculus I needed for my degree. I have forgot a lot. Professor Leonard makes it enjoyable to learn (some stuff) and relearn a lot of stuff. I was always was more interested in the mathematics then the physical sciences stuff. Thank you so much Professor Leonard.

[@Jerry-zf3ip]

man, professor Leonard is one handsome man.

[@tutorJ485]

I started watching your videos a year a go, starting from intermediate algebra. Now, I have just finished Integration By Parts. What a journey with the greatest teacher ever. I thank you so much!

[@pianogirlsmiles]

I always remembered the integration by parts formula by calling it "ultraviolet voodoo". I just love ultraviolet voodoo using LIATE: logarithm, inverse, algebraic, trig, exponentials for find the order of what to name as u. Plus, it sounds like an Italian cheer or something. "LIATE!"

[@UnforsakenXII]

+Samantha Vranes Girl. Thank you so much for that. I'm going to use that until my death.

[@AshleySPerry-wu6fy]

how about I LATE ? sounds fun right?

[@moviesrecapofficial]

Only if you were my teacher I'd be doing calculus till eternity without taking a break! I love the way you teach Professor!! and let me reassert here, that you ARE actually my only teacher. I never went to some school for the past decade and I was just a medical student back in 2007. with these lectures i am going to resume my graduation this summer and that too with calculus requisite. I'm drenched in gratitude, respect and thanks for this favour. You truly are amazing.

[@CampingINurMOM]

@ProfessorLeonard is by far the most in-depth and relatable math instructor I've ever come across. Thank you for your work!

[@isobar5857]

The only I know who gets happier as things get harder...I give you the inimitable Professor Leonard. He who has no equal.

[@Tyler-ke3eb]

I’ve been using youtube videos as study guides for the last year in math classes and I have never found another instructor who can explain so clearly why techniques work and how to apply them. thank you!

[@thericate]

this guy is saving me

[@clearancejohn]

you got ur degree yet?

[@omaralmadani4580]

thericate did u graduate ?

[@jim7195]

When Cal final is coming and u knew its time to come back to Prof.Leonard's lectures

[@follklor9976]

same thing here man that was best i ve ever head good luck with your exam

[@Rick_Sanchez_Jr.]

This has helped me so much as far as grasping this concept better as opposed to how our professor has explained it. Thank you for helping everyone learn Calculus, you are literally doing the public a service by possibly making people into future engineers and scientists.

[@riarajkumar8400]

Hi professor Leonard,I am from Trinidad and Tobago and I just wanted to say thanks to your videos for helping me pass my last course needed inorder to graduate with my Bsc in Education-Natural Science-Biology major. I passed Cal 1 .. so i crossing the stage in November.. so thank u sooooo much.. your videos and explanations are excellent and i really do hope i turn out to be like you.. an amazing.. life impacting educator in the education sector. You make a difference .. Thanks for the great content.. also.. u are very appealing to the human eyes 💪😏 thats why i loved ur vids 😂😂 LOVE FROM TRINIDAD AND TOBAGO❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤❤

[@nazombie7935]

Thank you professor Leonard! I am taking Calculus 2 this summer in a 11 week course and this video helped me kind of understand one section we will go over on June 6th. I am getting started learning early to be head of the concepts.

[@abrahamrosales5791]

I was having trouble with how to do this. Your teaching style was exactly what I needed.

[@Savage-do3vz]

Honestly, one of the best math teachers I have seen, you deserve some props prof. L :)

[@yeyovision1324]

Professor Leonard, thank you so much. After watching your videos, I feel confident I can tackle any Calc 2 problems. One of the best Math professors I've ever seen. I would have loved to take his classes, I imagine their better in person.

[@reubenwilliammpembe667]

8 hours ago I was confused during my class but now I am better thank you Sir #Respect!!!

[@swolby9230]

I took a long hiatus from Calculus while in college and reviewing these concepts is essential. Thanks for being great.

[@henrykolberg2234]

Thank you so much for these lectures, taking calculus ab as a senior in HS and trying to take the BC exam, lectures are explained well without dumbing down the actual calculus, keep doing what you’re doing!

[@KamSmooth]

You deserve the world. Preciate you getting me through calc 2.

[@sonwabomakinana7962]

The Senior Lecturer, Lecturer of the Lecturers thank you sir, much love from South Africa

[@leelah.1405]

Thank you from another one of your fans from India, didn't realize there were enough of us that your students know we exist lol

[@johnbertortega5086]

I watched this video because Our professor is having a hard time to discuss ir because of internet connection. Thank you Prof. Leonard I want to became a math teacher because of your passion to teach. Gobless you sir.

[@allysarahmarie8352]

I wonder how many F's he has changed to A's?

[@maksymandrzejdrzyzgiewicz5096]

Or how many E's he has changed to V's? :D

[@Shadowbrothe]

Mine, absolutely, I went from not getting it to I can do it in my sleep! I finished Cal1 with a 97%, excited for what he can provide for cal2, cal3 and linear algebra. Please everyone that can contribute to his Patreon, Professors like this are so rare and we need to support them!

[@relentless.resell]

@@Shadowbrothe yea he's clutch, saving me in calc 3 , linear algebra isn't too bad tho

[@geragal2008]

Superman is now a teacher, and not any teacher a math teacher. How cool is that, no wonder he can fly.

[@hockeynutt9434]

Pure example of how a Prof should teach and make sure Students follow.

[@minkim2576]

Amazing !!!!!!!!!!!!!!!!!!!!! I had a hard time to understand my professor's way of solving problems, integration by parts and other chapters too.... but now I am so happy!!! I can solve problems with Professor Leonard's way !!!!! amazing@!!!!

[@roku401]

With my independent study of calc, professor, you have brought me to new heights. Mind you, I am a senior in high school currently taking precalculus!!!!!

[@davidbrisbane7206]

As and actor the prof makes a great teacher, and as a teacher the prof makes a great actor. It is his super power.

[@shaboobis9283]

Absolutely incredible teacher, everyone remember to disable AdBlock on this page!

[@ejminmehranian1138]

i dont need to go to school anymore i can just watch this guy all day

[@SamuelLee-gw6wr]

I would like to say thank you on behalf of my friend who is taking calc 2 this sem. I recommended your playlist to him and his marks increased by a whopping 20% compared to calc 1.

[@smeargloid]

sooo GRATEFUL for this video!!! timestamps for myself for when I return to this video: 47:26 break 1

[@iamxareed]

i wish to see you one day thanks sir you are the best teacher i have seen in my life this year i took calculus1 and i get d but now when i start watching your videos i improved alot so i have exam next week on calculus 1 re exam and after that i will take calculus two in semister 2 thanks

[@aobfranko]

After spending 3 hours in class + 1 hours in a badly made textbook, 14 minutes of your video and I understand exactly what integration by parts is and I just finished all my examples... you're awesome thank you so much! :)

[@donaldjosuelopezbarrios8410]

Thank you so much for this videos, you are the best Professor in the whole world, make everything to seem so clear.

[@markreza3273]

You are the best at explaining!!!! Everyone should be very appreciative for sharing these free videos!

[@youngdomo9040]

I LOVE YOU SO MUCH THANK YOU YOURE GENUINELY SAVIG MY GPA

[@macedoyareli]

I have been struggling with this for so long and it only took this guy to explain it to me for me to finally understand. My calculus teacher sucks compared to this guy.

[@botpatch1]

My calculus teacher comes in, sits down next to his projector and shows us slides of problems with steps to do it and never talks. Walks out first before anyone can ask him questions - hallmark of a great teacher right there (good thing is he got fired for incompetency and about 200+ student and parent complaints)

[@MrBulat1990]

h1d3n1npl8in 51ght dang I can't believe they have teachers like that teaching an advanced math course

[@botpatch1]

Johnny Montana I think he was a good teacher back some what 10 years ago, but ever since he got his Tenure, he just stop giving a damn

[@EnvyBeatshamstring]

i can easily understand what ever you teach. You are the best teacher i've ever seen. I ve been watching your videos about 1-1,5 years the reason of my success are you professor superman :D !!

[@chadjohnson608]

Leonard: What’s the derivative of ln x Student: e Lmaoooo

[@marcusd430]

He thought about flipping it over y=x I bet.

[@boitumeloliholo7291]

Even after 5 years you are an awesome teacher, this is so relevant. You honestly make our lives so much easier. Thank you prof.

[@sardarbekomurbekov1030]

Thank you professor for clarifying the method for loop integral. That one buzzed me for a long time, but not any more.

[@epicdabber5262]

this teacher is so beautiful, what an amazing lecture! keep it up

[@fadinajor4817]

its so cute when he tries to skip a step at 33:38 but his heart cant do it so he still explains where the 2 came from lol.

[@juansandoval7271]

These videos have helped so much, I was just so lost with my professor, but you have saved me so much time

[@MyLe-zf5yl]

this is so much better than my class, my professor does yoga in the middle of school

[@Out1sSaidAsOat]

Fantastic teaching. Also, for those looking for the reduction formula 1:29:20 but i highly recommend the whole video

[@Peter_1986]

I am watching these videos as review even though I have other courses to worry about, just because Professor Leonard's videos are so addictive.

[@davisdiercks]

"you know you're being recorded right" "sorry" "don't apologize to me apologize to the people" me turning the volume all the way up trying to hear what he even said: AM CONFUSED

[@kajo2474]

He just went oh shit

[@read5869]

we started calc 2 from 7.1 that's the reason i clicked on this link :P @59:58 is exactly what i was looking for. Thanks Professor! you're a great teacher! s

[@ayushidave3067]

Wow! this video is absolutely fantasic!! I have a calc exam tom, and even though it is 2 hours long, I need to start with 7.1 and the way he teaches ALL the material, it is ALLL GOING TO my head. thankyou SO MUCH!!! far bettttttter than anyone I have been taught by!

[@Moonwalkerdrey]

you literally saved my life...i have a calc exam tomorrow and i had no idea what i was going to do. thank you so much!!

[@Don_Deppresso]

20:14 I actually pause the video and answered the question on my own And imagine how smug I am that I got the correct "u" for this problem, laughing by myself while everyone is asleep... Man... Engineering is a pain

[@dennisllopis2478]

22:11 -- "Whatever you see, put it in "V' lol. That was genius...

[@dalilarobledodebasabe191]

This is pure Au. Thank you professor Leonard.

[@macyhufford8586]

This helped me so much better then my calculus 2 professor needed this

[@bubblesxo]

i learn way more from the internet than going to class like shorter/simpler ways of doing things, tricks, mnemonics. not only is it way more convenient, but you can go at your own pace and hear things said in different ways to help reinforce information.

[@Tuffadandem]

This video is very helpful for Calculus 2. I wish to lecture in mathematics one day; you sir are an inspiration. Excellent video tutorial indeed.

[@la-dragoon8913]

USE LIATE when choosing for u and v. L = Logarithmic. I = Inverse Trigonometric. A = Algebraic. T = Trigonometric. E = Exponential

[@palashrajput428]

I think it's ILATE