# How to Integrate Using U-Substitution (NancyPi)

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Published on August 25, 2018 by

Follow Nancy on Instagram: https://instagram.com/nancypi

For my video on the BASICS of INTEGRATION, jump to: https://youtu.be/e1nxhJQyLYI

With all u-substitution integration problems:

The FIRST STEP is to pick your "u". The best choice is usually the longer x-expression that is inside a power or a square root or the denominator, etc (in an "inside function"). Set u equal to this x-expression.

The SECOND STEP is to find "du" by taking the derivative of the u expression with respect to x. For instance, if you have u=3x+2, your du would then be du=3dx. **NOTE: Remember to include "dx" at the end of your du differential expression.

The THIRD STEP is to substitute u and du into the integral everywhere in place of x and dx. **NOTE: if your du does not perfectly match what you need in order to completely substitute before integrating, you must rearrange the du, or sometimes rearrange the u, in order to fully substitute before integrating. For an example of each, see example #2 (time: 8:21) and example #3 (time: 17:15).

The FOURTH STEP is to integrate, remembering to add "+ C" at the end since you integrated an indefinite integral (no limits). The du goes away when you integrate.

The LAST STEP is to "back-substitute" by replacing everywhere u appears with the x-expression that you chose u to be.

For more of my math videos, check out: http://nancypi.com

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• No jokes from now on. ITโS STUDY TIME

• yes. integraaaaaaaaaaals

• Awesome as always

• Hek yeaaa this is what I exactly what I needed to refresh for my calc 2 .. NANCY YOU ARE AWESOME… THANX BUT IF IT’S NOT TO MUCH TO ASK CAN YOU PUT VIDEOS ON CYLINDRICAL SHELLS ROTAITNG ABOUT X AXIS

• Stanley Miranda ikr she is๐๐

• I hated that so much. It’s the reason I don’t tutor calc 2.

• That stuff along with the optimization and related rates made me regret taking calculus

• Just Google Shell Method

• Thank you

• good luck

• 17th like!

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• Got em

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• Next Video Suggestion: Calc 3 – Scalar Multiples (Vectors) and Parallel Vectors

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• That was seriously satisfying! A phrase i never thought I’d utter ๐๐

• ๐ค๐ค๐ค

• Nancy can you please make videos on CS Algorithms ?

• Algorithms for what?

• +NiHaoMike which are more popular and most of students want like, Algorithms for CS !

• Can u do scalar multiples, vectors

• Thanks for posting a video about integral
Cn you post more videos on integration I love integration

• YES…….Nancy I am one step closer to winning a Nobel prize >:) Thank you

• Xavier Rodriguez v

• omg i have a quiz on this on monday thanks nancy!!

• how did the quiz go?

• i guess it went well but my teacher lost my quiz and gave me a 0

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• Pls discuss about hyperbolic functions๐. Thanks ๐๐

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• Karina De Leon corny

• @Anette Svea รsgรฅrd god has no place here

• Can you also make a video on integration by parts?

• Thanks a lot!

• Will we ever move onto multi variable calc? That’s where I got a D and lost my confidence in math.

• can you upload some videos on calc 3 topics?

• Topic : Integration by parts

• Its great .love u

• Nancy, the problem with these videos is that they are too easy, we are the “loyal subscribers”, therefore (because we are loyal) we have seen all your videos from *Mathbff* which is why you need to start doing more advanced topics. i love you, by the way, you helped me super much! :3

• Thanks for teaching me integration using u-substitution ..

• can you show how to take the first derivative in binary? on IDK, an 8bit integer function.

• Can you make an AP Calculus BC Cram video before the AP Exams?!?!? That would help so much…my teacher for AB was not the best at explaining this kind of stuff and I was lost the entire year

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• Why was this on my recommend videos? I barely got past grade school math hahaha

• awesome method , you explain very little points even , and a wonderful face expression…Allah bless you and more success…

• Math is supposed to be highest order of understanding with ‘reason’ but you still bring the stupid religion into this. You should be smart enough to understand that the religion is created by people just a few centuries ago. I hope you become very rationalistic and modern. Any idiot is qualified to speak about religion. But not every idiot can do complicated math. Elevate yourself above idiots.

• If you were to build an Aeroplane based on your logic it will never take off the ground. You should have that sense if you have the capability to do math. Yes math is a language but unlike most languages you can only speak it if you build knowledge like a Pyramid. Unlike Religion where you can keep blowing from your arse like you did above. STOP. JUST STOP thinking with your religious head. Show nature that you are not stupid brainwashed idiot whose predispositions are preventing from elevating to a higher level. Show that you CAN.

• When she explains something complex, suddenly it becomes simple. Teachers around the world need to take this girl as an example.
Please keep up the amazing work! You got my support until the end!

• Solid Chrome i

• Thanks to you and your old channel, I passed Calculus 2 so I don’t really need to watch this video anymore. But I still wanted to give you the recognition, views, and likes that you deserve! Please keep the videos up. You are helping so many of us struggling students!

• Hello Nancy, je suis un franรงais qui regarde vos videos. Do you speak french?

• Hi, I was wondering if you offer tutoring? Does anyone know if she offers tutoring

• Could u make video on how to integrate by parts? Please

• literally helped me more than my calc professor…

• Can you do Integration by parts?

• you should bill GSU for my tuition!

• Iโm paying \$2k for my Calc 2 class. Attended 2 class of 4 hours and thought I would drop the class. Now Iโm watching this video and I feel like I can tackle calc 2! Thank you, youโve helped me since pre-calc

• Hey Nancy, if you could cover some topics from Calc 2 I think a lot of us would appreciate it. Seems to be a bit more strenuous and less intuitive than calc 1. The way you explain these theorems in a simple manner and at a rate that isn’t too fast nor too slow really helps you standout among all the other “math wizards” on YouTube (It’s also a breath of fresh air to be taught by an extremely attractive female instead of my grumpy ass professor, so thanks.)

• 11:46 baby like kawaii *-*

• Nancy can you make a integration by parts?? I am struggling and my professor does not explain it to where I can understand

• She breaks it down for us simple folk. Better than my professors.

• Thanks it helped a lot…

• Who are you married to or dating; lucky guy. Beautiful and smart; however, I heard statistically smart girls tend to be single…

• Hands down best instructor ever. Also very attractive. Thank you Nancy.

• Oh thanks so much!, this part (18:43) is what drove me crazy for about 1 week, the professor didnยดt really explained the way it was supposed to be. I was assuming the “du” was always written as “(du/###)=dx.” I can certainly tell, I consider you the English version of “Julioprofe” ( he is well known as a great math teacher among spanish speakers). Thanks again!

• great video! i was looking for excatly this example!

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So much
I was so lost (in calc)
And now I am found

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• Definitely worth my time.

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I subscribe yours channel, I hope you will do the same.

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• Thank you so much Nancy, you are a godsend!
Saving us all from the terrible math professors who rely on the fact that they have tenure and don’t give a shit anymore.

• for the first one why does du simply go away shouldn’t you have to integrate that as well?

• Nope , it just goes away

• 5 hours before my paper, I was clueless… 4 hours before my paper and I’m already quite confident… Thank you sooooo much…

• lifesaver

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• A blessing ๐๐ผ I have a gateway exam on Friday

• you just made it clear, thank you so much

• Hi Nancy, @18:50, why don’t u use the derivative to correct it like example 2?

• Patrick Caspers Iโm not Nancy, but it would simply not be helpful to get du/x = dx/x because then youโd be stuck with an x, which you do not want because you only want to work with u du. The point of this technique is to find a way to get rid of all xโs and have uโs instead. Hopes this makes sense ๐

• @Vily Rose thank you very much! I was wondering why because the rest of the sum seems to be the same

• I love this woman!

• Hello, for the first example: 3x^2(x^3+5), can’t i just multiply out the brackets to 3x^5+15x^2? Why is the solution then different?

• DanTheMan 92 The original problem was 3x^2(x^3+5)^7. If you foil (x^3+5) seven times THEN distribute 3x^2, you should get the same answer.

• i love the way you teach……..

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You are innocent as a bunny ๐ฐ

• Excellent videos but light colors have low contrast and can be hard to see.

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• Love you!

• Her attitude in teaching is probs my spirit animal. It’s like you’re so done, but keeping it together. ;A; Lezgo

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• Thankssss fot this videoooooooo

• I’m so glad you were able to get your original MathBff videos onto your new channel. NanciPi > MathBff

• thanks a lotโค๏ธ now i can do it on my own๐ญ

• Thank you very much Ma’am Nancy. You’re so beautiful, I LOVE YOU <3 THE BEST CALCULUS TEACHER!!! EVER!!!

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• Yo your voice makes me fall asleep. Thanks for the lesson tho

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• Nancy, I love you, thank you so much. Nobody has explained me as well as you do about how to choose my u expression and what du was. Iโve used your four models in this video to do my homework with similar exercises. Thank you, now I better understand my book.

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• 6:17
‘If you dont remember how to do that… click off this video right now’

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• Ooooh soo nice of u
Thanks .
I like ur videos u make math so simple

• U goddess!

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• I just noticed how in her point of view she writes all the equations backwards like as if its nothing…..

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• how do you write inverse????????? magical

• Underrated. This lady deserves everything. Thank you I fell like ive never understood this before and you make it so easy

• This vid taught me so much better than my prof could. He just does the math while we watch without explaining it. So I leave class everyday without a clue of what I just witnessed.

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• THANK YOUUU!!!!!!

• precisely what i needed today. you rule!!

• Question: how do you write on that. Is that a clear board and if so did you learn to write backwards or something? Im sorry does anyone else have this question too. Like it bothers me just cuz. I know Im weird.

• I think that she just writes normally on the clear board, but then in video editing just mirrors the image so it appears forward for us and not backwards.

• Can I take trig functions as u if not then y??

• Watching this video really took the work out of studying

• She is smart beautiful and calm I like her so much

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• Once again you’re saving my life in Calc 1 right now Nancy

Bless this channel

• why do i feel like shes trying to seduce me at the same time she’s trying to teach me?

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• Awesome girl. luvu nd your skill ..

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• you are an amazing teacher. saved my life…

• thanks

• You rock! I got more out of this video than I have in the last two weeks of class.

• Lol, you are so intelligent and beautiful, I wish I could integrate you into my life, haha.

• Hahaha

• “it’s OK you don’t like MAth, nut you can like my video “, I died ….Only if YouTube has love as well, I’ll give them all to ya ma’am

• literally come here when my maths teacher talks nonsense

• Does she have anywhere where we can donate to her for providing these wonderful videos? Made this so easy to understand and was way more helpful than my professor. Thanks so much for making such quality videos and going step-by-step. It makes those of us who are taking classes a decade after we finished high school much easier to understand! If you have anywhere I can donate to you for your time/help I would love to know!

• was hoping for a different kind of donation account

• @raptorgod77 of course. Monthly subscription to Patreon while I was taking calculus. Got an A in the class with a ton of help from this channel.

• Marie B what comes with paetrom

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• Is she writing the whole thing backwards?

• you cant have a du in the numerator of a fraction, its strictly a subscript.

• thanks NacyPi Sensei I wish you were my professor

• Bless your soul. I was beyond frustrated and nearly in tears. It was something simple I was missing, and I found what it was in your second example. Many, many thanks.

• A am from azerbaycan;very beautiful

• Plz show us how to do this with sin cos and tan

• This is literally the most painful video to watch.

• you’re hot, i can’t focus

• This is the best explanation on how to use u-substitution – always struggled with this one…

• I know the math already and yet, here I am

• 13:51 to 13:55, that switch up tho lmao. Thank you for this!!! Videos like this are timeless

• Do you write up side down?

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• marry me

• I had (4x+1)power to 7. Like got answer close but not like as in video,

• I figured it out. Great explanation in video. ! !!!

• cant we solve the last question as tanxsec^2x dx????

• I love how in a calculus video she is having to explain why -0.5 + 1 = 0.5 XD

• Really good Video!
Thanks for being so thorough! (:

• Can you integrate me? ๐คฃ

• “Are the videos from the 2006 really helping???, yes YouTube advertisment it is, now leave me alone jesus.

• WHY FIGURE IT OUT FOR FREE WHEN YOU COULD PAY US?!?

• This is definitely useful, but to be fair, everything I’ve seen from NancyPi is both more recent and far higher quality than anything you could find on Youtube 13 years ago.

• the name JESUS, is not curse word or just a random sentence filler, it is the name of utmost power and efficiency. Don’t abuse, misuse or take it in vain. Seriously, not funny!

• OMG SAMEEE hahaha

• Dude, its a year later and I’m still getting the same ad lol

• Thank you teacher

• Where did the 3x^2 and dx go in the first problem? Why does it disappear just because we substituted?

• Yes.

3x^2 dx = du

• Thank you, holy shit you are great at teaching

• You’re never allowed to go away, Nancy! I swear, I can struggle with a calculus concept for hours, but watch just one of your videos and suddenly everything is crystal clear! You make it so easy and I love your teaching style! Thank you!

• Worked these examples along with my problem set. Made it very clear thanks alot.

• Sagolasin baci

• Would totally substitute U for my X.

• ๐๐๐๐๐๐๐๐

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• ๐๐ฆ

• I was thought calculus about 30 years ago.it was a mystery up to now.you makes it so easy that I understand lt.pls let me donate for your time..
Many thanks for your generous knowledge .Elias Kidane .

• I feel like sheโs holding her breath๐

• 2 days before the exams. Lets get this bread

• In the last exercise, why didn’t she replace dx with -du/sin(x)?
It’s what has been bothering me the most, sometimes it looks like you’re not supposed to replace dx

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• you are perfect in your explanations.. Seriously! Plus could you please do gps explanations.. ๐

• Hi. Watched a few of your videos as Iโm currently doing an OU course in UK. They are fantastic – so easy to follow and much better than any other sources. Thanked you by starting a Patreon contribution. Keep up the excellent work please ๐

• for 2nd question shouldnt 4 be taken out instead of 1/4 ?

• what else can you show other than the easy stuff

• It is in deed helpful. Thanks a lot

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• How to do anti derivative of x+3/x-3 by u substitution?

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• kiss

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• Are you planning on making more videos? There’s a new girl on mathbff. I couldn’t figure out why you were harder to listen to now….and then I realized that wasn’t you….ma bad. Lmao

• @NancyPi – Could you explain why in the indefinite integral of f(x)dx, the function and dx are being multiplied by each other?

• dx is the infinestimal amount of anything like length when you are looking for an area like parabola. Then for finding area, you need to sum up all the product of height f(x), and dx’s or in other words, integrate them. dA = f(x)dx. dA means infinitestimal area. f(x) = height of thr strip and dx be the width of the strip. Assume it is rectangular strip so back to geometry, A = hw

• Thats for definite integral by the way

• In indefinite integral, theres an arbitrary constant C shown in the video. You can find its value depending on the conditions given on the problem. You can use this in physics like kinematic equations.

• btw thanx for video and i got how she is writing like that ! at first she writee like we write and using editor she flips the video horizontally๐ or may be she is writing this backwards๐คค๐ฑ

• Yo how tf she writing backwards

• learning and loving at the same time.best teacher….

• thanks

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..

• Complete pack..

• I love the content, but god damn. The endings are so cringy.

• I wouldn’t substitute u as a teacher

Ok, now i’ll study, no more jokes from now on

• thanku so much you helped me in understanding this concept…

• Is this calculus or algebra II?

• Calc

• You are gorgeous

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Everyone!

• Nancy integral = Smart , Nancy derivative = Beautiful !!

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• “What happens when you have a trig function?” Well, I simply cry. However, this video was beneficial.

• Can u increase ur speed in talk and we are steadying calculus plz donโt bother yourself and calculate 1/2+1 you are the best thank u โค๏ธโค๏ธโค๏ธโค๏ธ

• I watch it with the playback speed at 1.25% to make it faster ๐

• Playback speed 1.25x

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• I wouldn’t have gotten through high school without you, now i’m in university and you’re still my lifesaver ๐

• 6:37 where did the 8 come from

• Differentiate U^8 / 8 and that will give you U^7. Integrating is the reverse of differentiating.

• Blink twice if they’re holding you hostage.

• Spray some pepper if they are causing you lust. – The Holy Fuck1ng Bible.

• @Bob Pickleson I am sure writing mirrored on a glass is not satisfying.

• They are holding her hostage, on the other side they have a gun to her and the only way she can stay alive is by doing calculus.

• @Valentin A. she actually writes normal to her perspective, then they flip the video when editing. you can tell because her expo marker letters are mirrored

• I thought this comment was kpop stuff etc

• I like how she looks at the camera and smiles at us when she finds the solution.

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• This helped me sooooo much thank you for making this video I missed the class on this and I couldnt get the notes to do the homework but this video really helped me understand this topic thanks.

• leng

• Loving how the video description has the links to different types of problems. SO HELPFUL!

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• ููููููู

• Awesome!!!! How do you do that?????!!!!!
I also have a youtube channel but I use a chalk board!!!!!
#mathsolveszone

• HI!!! 1k likes 1k comment lets date????

• Damn, cant believe I haven’t found this sooner.

• can we just face the fact that she is writing the equations backwards???

• Thank you so much for this wonderful video.

• Not specific to anyone, but the professor always sucks. Youtube always make more sense than the university. So why I spend so much on tuition and study on Youtube in the end????

• Gee, this video helps me so much. Appreciate!

• am i the only one getting distracted by her beautiful voice

• great ! THANK U

• This was very helpful. Thank you!

• could be the final answer for the last question is ln|2(cosx)^2|+c right?

• This may be useful:

• that smile before every fast forward is breathtaking.

• This was a calculus video?

• What type of voodoo black magic. The hell is she writing backwards!!?

• Very nice video is there any WhatsApp group

• Gets serious at 13:52

• I’m too distracted by how pretty she looks; therefore, I have failed to grasp the overall methods surrounding the topic, and thus have failed in my pursuit of knowledge.

• U are truly an X pert teacher….thanks for the help ๐

• I stay up late thinking if she really is writing backwards or if thats a trick.

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• I aced my calculus class before this fucking video came to an end

• ty

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• One Word… Lengendary!!!

• You are a lifesaver

• She needs like some fuckig back ground music or something

• WOW
Thanks so much for your semple and nice explination

• Maths explained super. Can you load. Fluids, solids, and thermal subject lectures.?

• Great video, very helpful…thanks!!

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• I believe t is the standard letter

• 54 previously difficult integration sums disliked the video

• i love you nancy, will you marry me?

• Iโm trying to figure out is there a clear board in front of her and sheโs writing backwards?๐ค๐ค๐ค

• Yes I got it easily……. you r good at teaching…

• How do you write backwards๐ค

• Really i like math + i like your video to = so i start fall in love with math

• OMG! This video is very helpful!! Thank You!

• What do “u” and “du” mean? What are those? And what is “dx?”

• David Ullman dx means with respect to x in an integral that is you are integrating with respect to x. u is something you define from the original integral and differentiating u gives us du which we re write in the original integral

• Awesome

• I dislike my calculus teacher to depths that Iโd rather not mention. Thanks for the immense help.

• Thanks for going slow and in a understandable way. Please keep making such tutorials.

• If you were looking at the math, I have news for you

• ูุฑุญุจุงุง
ุงุฑูุฏ ุชุฑุฌูุฉ ููุบุฉ ุงูุนุฑุจูุฉ

• it was hard for me to concntrate at the begining, she is so pretty, and smart as hell!! SHE is a diamond.

• I think the most impressive part is that she’s doing this while writing backwards. I can bearly manage it forwards

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• wow, best teacher ever. its my third year studying calculus but after seeing your video, i understand it perfectly. thank you so so much.

• I figured out how you write backwards ๐
You write on a transparent glass sheet and record, then you edit the video and flip it. Simple yet ingenious

• u r du best

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• The best teacher I have ever seen

• Didn’t learn a thing because I was to busy picking my jaw up from the ground. Wow your pretty. Second time around I learned everything I needed to from your video, thanks!

• My teacher was right, she is cute.

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• Kawaii :3

• No I don’t have a du I have a DUI after trying to learn this.

• She hot

• “Function forms.” Nice. (undoing chain rule.)

• d (U^8)=8d(U)รU^7 #8 U^7 !!!!!!!!!!!

• Hi im mohsin bs student so
Will u plz help me integration of “underroot tanx”…?

• I was looking at a problem with U substitution and couldn’t figure out why du disappeared in the solution. I’m so glad you explained it as reversing the chain rule. Thank you!

• 8:17 Please answer me, why is it ok to completely ignore the 3x^2? I mean it was like it didnโt even exist

• John Landon Miller du = 3x^2 dx thus both 3x^2 and dx are replaced by du when she re writes the integral in terms of u

• Fen boii yea I understood that now thanks

• Watching this while doing problems on inverse trig functions. Don’t know why but at least ILATE.

• Nancy you’re no fun my dear

• ty

• hey nancy the end ans. could be also 1/2(secx^2)+c

• Thanks for the refresher. Great explanation Miss Nancy!

• Thank you soooo much you truly are a blessing.We really appreciate your work please keep making more videos.

• Just spent 26 minutes watching this and now i have a better understanding than spending 2 hours sitting in a lecture. Cheers Nancy!!!

• you are one of the main reasons I got an A* in A level Maths

• I finally understood U sub after spending 2hours studying it and 3hours in lecture ๐ thank you so much great video

• Oh wow that’s smart as hell. I’ve been wondering how she is able to write mirrored on the glass so well. But you probably right normally and mirror the video!

• Nancy, I keep having _oh so sweet_ daydreams whenever I watch your videos, as is evidenced by the number of times I have to rewind. If you were to do it all in real time instead of in video format, I would have been *totally* lost! ๐

• Honestly GOD BLESS YOUR SOUL๐ญโค๏ธโค๏ธโค๏ธ

• Hello mam,
The engine speed where the integral of max. Mapped torque is 51 per cent of the whole integral between ๐๐๐๐๐and ๐95โ. there are values from n to 95 n

• all waya great

• why do people like her not have millions of subs, they’re doing more good than rice gum and jake paul

• if she dabs she will get famous

• Think about the potential audience size. People who are using YouTube specifically for Calc 2 versus people who are using Youtube to consume “entertainment media”, the market sizes of those two population groups are wildly different, and thus, the subscribe base is usually commensurate with that.

Not saying it’s wrong or right, but that’s why.

• Hot girl

• Nancy Pi, I have no clue as to why 76 people disliked the video lesson, by the you are great. but, now I remembered that math is the leading cause for low IQ of this nation and that alone causes people to have scrambled brain also the urge to go pee pee.

• Nancy, When you explain, it is clear as crystal. You are beautiful!

• beauty with brain

• These videos are so good they’re part of the lessons here now – many thanks for your great work.

• i go to one of the highest ranked universities (in the world) and shes better at teaching than my calc prof. thank u so much girl

• I am taking AP Calc Test AB as freshman. This helps so much because I am self taught and have no teacher. Thanks so much!!!

• beautiful with brain

• thank you so much nancy

• NancyPi: “Now this is looking like you know how to integrate”
Me: “ha you think i know how to do this why else would i be watching”

• These lessons are so enjoyable, I am having fun re-learning my calculus again even though I don’t need it in my work. Strangely de-stressing, keep up the good work!

• Once again NancyPi to the rescued to explain a concept much more simply and in half the time as the Prof that I pay..
So once again, thank you so much for your incredibly helpful videos!! You do such a great job.

• Your ability to write in mirror-image wise never ceases to amaze me.

• Jansen Tanu idk if this is a joke but Iโm pretty sure that she just writes it normally and then flips the video before posting it

• Didn’t even come here for maths ๐

• I’m a local maths teacher, geez ur no. ur getting pumped

• Very nice Nancy, thank you

• But on a serious note, I would wife you. And on a more serious note youโre doing great this is very helpful

• Damn shes cute ill never get a girl like her ๐ค

• whiteknight

• Very effective video.I’m….

• So does she write backwards or something ๐ง

• You are awesomeโบ๏ธโบ๏ธ

• Thanks for the explanation, better than my professor’s. It was like a free lecture, without the need to fetch a tutor that’s busy with hundreds of students. You cleared up some of my confusion, such as how dividing fractions is the same as multiplying by its reciprocal.

• You have no idea the blessing that you are to me!!! Getting a 73 in bus calc…..you are helping me so much!

• Thank you Nancy, you are just perfect in what you are doing please keep on

• i wish you could teach me some

• excellent lesson and shes cute too ! (:

• Amazing as usual but you’d thank me if you watch this video at 1.5x

• the integral of x/x+2 was on my test and this helped me

• I simply don’t understand how you remember all this and methods, so many people can do this, I unfortunately can’t, algebra just leaves me cold, just how my brain is wired I guess!

• Anyone else getting ready for this AP calc test?

• no

• Perfect explanation, many thanks!

• I’m a proud subscriber! This young woman is certainly easy on the eyes, has a nice voice and demeanor, and most noticeably is very intelligent and knows how to convey her knowledge in simplistic, understandable ways.
Thank you Nancy, you’ve certainly helped me out in a lot of my classes!

• wait guys is she writing backwards so we can see it forwards hmmmmmm.

• God bless you Nancy

• find the indefinite integral by using change of variable method:
3โ(3+7x)dx

• So, in this case, you have the (indefinite) integral of 3 * sqrt(3 + 7x) dx. What might help a little bit, to start off, is to pull the 3 out in front, first, since it’s a constant multiple.

NOTE: I will leave off the “+C,” until the very end of the problem, which we need, because this is an indefinite integral.

Then you get 3 * (the (indefinite) integral of sqrt(3 + 7x) dx).

Now, let’s take a look at (the (indefinite) integral of sqrt(3 + 7x) dx).

Now, when we integrate by substitution, we typically substitute for the inner-most part of the function, which, in this case, is the 3 + 7x, since that is the expression inside of the square root. We also notice that when we take the derivative of 3 + 7x, we just get a constant (7). We differ by a constant factor, when we take the derivative, but we can work our way around that, fairly easily.

So, we start off by substituting for the 3 + 7x.

Let u = 3 + 7x.
Then du = 7 dx.
=> (1/7) du = dx.

(In this integral, however, we have the dx, but we don’t have the 7. Hence, we need to divide both sides (of the du equation) by 7, which is the result above.)

At this point, our integral becomes (the (indefinite) integral of sqrt(u) * (1/7) du). The (1/7) is a constant multiple, so we can pull it out in front of this integral. We get (1/7) * (the (indefinite) integral of sqrt(u) du). We can re-write sqrt(u) as u^(1/2). Then (1/7) * (the (indefinite) integral of (u^(1/2)) du).

To find the antiderivative of u^(1/2), we can use the Power Rule for Antiderivatives, since the exponent on the variable, in this case, is a number, where that number is not equal to -1. The Power Rule for Antiderivatives tells us to bring down the variable, raise the exponent on the variable by 1 (i.e., add one to the exponent), and then, in front of that, multiply by the reciprocal of the new exponent.

In this particular example, when you raise the exponent by 1, you get a power of (3/2) (i.e., because (1/2) + 1 = (3/2)). We also know that the reciprocal of (3/2) is (2/3), so that’s what will go in front of the variable raised to the power.

(1/7) * (2/3) * u^(3/2)
(2/21)*u^(3/2)

We started out in terms of x, so we need to finish in terms of x, and so we go back to our original substitution, now (We replace u with 3 + 7x).

(2/21) * (3 + 7x)^(3/2)

Don’t forget that we also had the 3 (which I wrote, below, as (3/1), since we’re multiplying it by a fraction (i.e., (2/21))) that we pulled out in front of the integral, at the beginning of the problem.

((3/1) * (2/21) = (2/7))

(3/1) * (2/21) * (3 + 7x)^(3/2)

(2/7) * (3 + 7x)^(3/2) + C

After all simplification is done, we get (2/7) * (3 + 7x)^(3/2) + C.

• Now, let’s take the derivative of our answer, and check.

(d/dx) ((2/7) * (3 + 7x)^(3/2) + C)

The (2/7) is a constant multiple, so it stays put. Then, to take the derivative of (3 + 7x)^(3/2), we have to use the Chain Rule (in combination with the Power Rule) (Bring down the exponent and the variable, then subtract 1 from the exponent, and then, by the Chain Rule, we also have to multiply by the derivative of the inside).

(The derivative of (3 + 7x)) = 7

NOTE: I wrote 7 as (7/1), so that I could multiply it by the other fractions.

((2/7) * (3/2) * (7/1) = 3)

(2/7) * (3/2) * (3 + 7x)^(1/2) * (7/1)

3 * (3 + 7x)^(1/2)

We can re-write the (1/2) power as a square root.

3 * sqrt(3 + 7x)

The derivative of the “+C” is zero (0), because C is a constant, so we can just leave it off, when finding the derivative, because we’d just end up adding zero (0).

Lo and behold, we got back the function that we started with. So, we know that our antiderivative is correct.

• Really glad I took the time to search this up and find this video because it made substitution so much clearer.

• Thank you so so much.. although no 2 was kinda a pian for me I’ve understood..thank you so much…

• Thanks this is so helpful

• I hate the way she speaks but i love the way she teach

• Cesar Godinez she has some weird pauses but Iโm pretty sure itโs just her pausing, trying to decide how far to dumb it down.

• blink twice if they’re holding u hostage

• My final is coming up and she just taught me all of math analysis in one night better than my teacher has in a year.

• thank you very much. . i’m styding now amolst 11PM,,this really helps me for the test tomorrow

• I watch your videos in a mirror
Thank you so much

• 25:35 “Calculus is everyone’s favorite *nervous laughter*” HAHAAHAAHAAHAHAAHH

• Your videos are great help to me
Thank you ๐

• You’re the real MVP

• Why does she smile?
Distracts me

• i love you nancy pi for your way of teaching and expression.

• thanks a bunch very machhhhhhh

• What a mem๐๐๐๐๐๐๐๐๐๐๐๐๐๐

• ๐๐๐๐๐๐๐๐

• Men you so beautiful ๐

• Bhai log kon sums ke bahne mem ko dekh ne ata he ๐๐๐๐๐๐๐๐๐๐
Lile here๐ค

• Thanks for making this content to help people with math! I followed along with your videos after using other youtube channels to help me get through calc 1! Finals soon!

• Can u speak louder???๐๐

• Nancy I can totally integrate U in my life

• You are amazing Nancy. Thank you from Italy. Youโre helping ppl all over the world :)))

• 2:28 wrong

• You have properly explained what my 2 instructors were never ablet to explain. The U-substitution was a nightmare to me. Thanks very much for the video… Keep up the work….

• super duper ,well explained

• nancy you bastard

• it is basically integration by parts

• wow thank you so much, this was actually helpful and I could understand it completely. I have kind of been getting the gist of it, but it wasn’t until this video that all my questions and confusions were cleared up. THANK YOU!!!

• 3:50 what is it is at the top of the fraction?

• Substitute ex by you ๐

• You m’lady are not a mere mathematical model–you’re a theorem.

• Holy… I finally understand this after hours of trying to learn

• Noice

• Beauty with brains. I am smitten.

• Thank youโคโค

• Thank you, great video, I like the simplicity and structure

• POTENTIAL CLARIFICATION IF YOU ARE STILL CONFUSED: On thing I personally kept getting caught up on is why these equations were “a perfect world scenario” and why that worked. Simple approach/ phrasing fix for me is, when you find du in relation to x and dx take that equation and specifically solve for dx. Then substitute that into the integral for dx. Take the trig equation at 23:00; solve for dx=-du/sinx, when you substitute that whole statement in instead of stopping at sinx dx = -du and assuming. You will have a sinx in the numerator and the denominator that cancel each other out. It should be the same answer in most cases for the perfect world scenario. If doing that creates issues like another denominator with a polynomial or a root function to deal with you could then take a step back and try to single out the inverse of the numerator the way she did, but that shouldn’t happen. Also, what I said might be a bit more time consuming if that issue can happen, but it just seems like a mindset/ approach that’s a bit more algebraically sensible to someone coming into this. It might be a practice thing or just the way I see problems personally, but eventually you should be able to see those patterns before hand the way Nancy did.

• Petition to give James Stewart’s 33 million dollar mansion and gift it to NancyPi because real math teachers deserve mansions, not scam artist textbook authors

• She is so smart and pretty

• you are so beauty! as well your explanation that is also enhancing beautification!!!

• AP calc today in a couple hours. And Iโm watching this, wish me luck

• How does this beautiful and smart girl write a mirror image of equations so well wtf

• She doesnโt …. itโs originally shot with her on the right side writing on the left, that image would be in reverse to us as is, so they flip the image, she goes to the left and the writing appears correct. Whatโs blowing my mind is that she is a lefty and proves the point that lefties are great with math …. definite truth to that one.

• Rob except then the math would also flip dude lol.

• @Bob Pickleson u guys are negative iq she is writing on a clear board in front of her then she mirrors the vid in post production so it looks normal to us

• @Travis Ritteryep

• I would love to support you for all your hard work. However, would prefer to do it one time only and not subscribe and share personal details on any website. As MIT graduate I’m sure you’ve heard of Bitcoin. If you have a wallet please share it and I would be happy to donate. Kind Regards

• Now I understand intergration you are a STAR Miss Nancy Pi

• Rendering error 0:27

• Damn, she’s good at this.

• Nancy, you’re such a wonderful teacher! You have really simplified the concept of u substitution for me! So much clearer now. Thank you so so much! Way better than my lecturer at university <3

• U have made me understand u – sub so perfectly that I’m also able to integrate complex functions… Thank u Beautiful๐

• I wish i have a future girlfriend as brilliant as you are

• You helped me so much ,you have no idea teachers should play your videos instead of explaining it themselves

• Videos are really helpful, you are great, thanks!

• play this at 1.25 speed, youโre welcome

• 1.75

• thank you sir

• No

• Nancy, Math

• man i can’t focus with that voice. are you teaching me or seducing me LOL

• I really don’t get it.

There are millions of teachers around the world. *Millions*. And here we have one young graduate posting YouTube videos that will be used for years to come, putting most of them to shame. Why read black and white books to learn this stuff anymore, when you can have a clearly explained video with sound, picture, and body language/tone of voice to teach you. Academia needs to evolve, badly.

• Thanos u so much.
Just kidding thanks so much.

• you are the best!! with your videos I reviewed my lack of calc 2 for my Differential Equations class!! Thanks for doing everything step by step and keep up with the amazing content. By the way, you are so beautiful without being creepy or anything!

• she’s rather good.

what is missing is applying videos with pure theory , so that the exercises are more thorough

• I’m so happy, this video made me see the light.

I was revising for my maths resit for my engineering diploma last week, was really struggling after studying integration by substitution, integration by parts, not getting it, then moving onto ODE’s & Taylor/Maclaurin series, all requiring knowledge of integration methods. I was really at a loss, watched your very well explained video. I have since decided engineering isn’t for me, start my first lesson to become a truck driver in 3 weeks provided my medical comes back clean.

I can pass every other aspect of engineering, but this pure maths just doesn’t work in my head.

• @NancyPi , wouldnt the integral on the third step of your second example with the fraction become an absolute lin function instead according to the integral rule?

• โคโคโคโคโคโค

• really u r g8

• i love you.. you’re so beautiful and smart… muah <3 <3 <3

• Lesbian??

• @Auhana 494 nope..haha..i have a boyfriend..saying i love u to a fellow girl doesnt mean a lesbian…

• @Evangeline Alabata ooo, i’m sry. Dont mind. I shudnt hav said dat๐๐บ

• @Auhana 494 its ok…

• So, basically, we just guess it, right?

• Maths is my favourite subject now

• I always thought you typed mirrored, wich is difficult, but you just mirrored normal typing with the camera ๐ฎ

• This was super helpful thanks!

• ohhhh yeeeeessssssss

• You are my secret crush on internet, I fall asleep listening your voice, your channel is the best I subbed in my entire life.
I have one question: are you lefty able to write mirrored? Because I am too.
Hugs from somewhere on earth <3

• butiful

• Very good video and explanations, but I’m vexed by your inverted writing! What witchcraft is this! ๐

• That’s the cleanest, least tedious presentation on u substitution I’ve ever seen. Excellent.

• That was epic!!!

• I wish my teacher can explain questions like you

• Thankyou for your awesome videos. The way you make us understand is so simple. Liked it ๐

• thanks for saving me from my teacherโs lack of explanation <3

• I’ve studied calculus and I’m a teacher. These videos on calculus are easily the best series on the topic I’ve ever seen. Nancy relates easily to the real struggles of calculus students, each step in the approach connects clearly to the previous one, and her set-up of the clear board looks awesome but is very effective and non-distracting. Beautiful work.

• WOW…your amazing. Just rescued me!!!

• Thank you so much ๐๐๐๐๐๐

• HOW IS SHE WRITING BACKWARDS THO

• ๐คฃ๐คฃ๐คฃูููุช

• I have never had a so competent and beautiful teacher

• How can I marry you teacher ๐

• Nancy – you explain everything so well. I wish that I had had a teacher as gifted as you when I was initially learning these concepts forty years ago. Thank you for all that you do. Please keep up your amazing work.

• Hi Nancy your classes are very interesting. I have almost 50 video the sum of my eyes and abbonnรฉs is not even worth 2% dun of your video,! maybe they will see your sexy voice or your beautiful eyes in my chain, Maybe the numbers of my abbonates will increase what do you think ..? I am also a matematician and physisian ๐

• Now I realize how beautiful subject is mathmatics๐๐๐๐

• Hi guys does anyone could tell me where we can use this calculus in real engeneering ? No kidding please

• u a whole princessss.

• I like Maths.

• Pretty pretty pretty pretty pretty pretty. If u were my math prof I’d never have cut my classes.

• ive watched SO many videos (most of them in german, they are usually not as good as the english ones) … and none were so clear and understandable as this one!! I dont usually comment under videos but thank you so much! in a way it did save my (social) life cause i hopefully dont have to retake my exams and waste my summer studying ๐

• actually +C is +C because, if the actual value is negative, +(-) evaluates negative. if it was -C and the actual value was negative it would be -(-) which evaluates positive. it is +C on purpose.

• you are incredible , thank you very much

• Man, this teacher is gorgeous!!

• You are the best Math teacher i ever had!

• Hello

• i would never substitute u.

• very intersting i am not native speaker and it is always n8ce to brush up some maths and also the math terms

• I’m so good in math and I can use so many short tricks to get the answer in 3 steps without that long explanation.

• if you are taking calculus LEARN THIS METHOD because you will see it again and it will save your ass!

• you are a marvelous teacher, tank you!

• Hello I love your teaching . I am a cambodian. I want to know about that you using program . can you help me

• this video is wonderful

• Thanks Nancy. Great class.!!

• Great

• they say it’s hard to find a woman that will be both beautiful and smart – here she is!

• Such a stupid comment.

• Well, I can’t make everyone happy

• @Los Daniellos B yes you can.

• ะัะปะฐ ะฑั ัะฐะบะฐั ััะธะปะบะฐ ะฟะพ ะผะฐัะตะผะฐัะธะบะต ั ะฝะฐั ะฒ ัะบะพะปะต, ั ะฑั ะดะฐะถะต ะฒัั ัะฐะฑะปะธัั ัะผะฝะพะถะตะฝะธั ะฒัััะธะป.

• Thanks

• Thank you so much for taking the time to make this video!!!!!

• This video really helped me understand much better.

• Thanks for your explanation

• So #1 it’s somehow 10x easier to learn from an attractive babe contrary to popular belief. #2: She looks like Violet from The Incredibles.

• #3 (and this is the big one): Is she straight up writing in reverse so that we can see things facing the right way?

• Thank u medam God bless you….

• NancyPi is my girlfriend and she is just like the square root of negative 100: a perfect 10 and imaginary.

• Lol

• @Joshua Runt no lie dude she’s fine but that’s it, 7/10 from me

• hahah, I like that!

• @kumar upendra I clicked your link frantically because I imagined my ‘perfect 10’ GF Nancy Pi might be there and she was not. ๐

• Hot with Brains ….. ๐โ๏ธ

• what is the point of u other tha simplfying solving for x?

• I love you

• thanks Nancy ily

• <3

• Awesome!

• What?

• Nice, u teaches well!!!

• I Love you Nancy and may be we could still!

• nancy you are not at power 7 you are at power 2 yourU

• nancy take you compute first the power you multiply by the 3*x power and you get a summ to integrate take care

• Nancy you explain nicely and i would like you explain me from closer

• creest Nancy take care to that too finger length!

• Nancy ho w does it go since the first time we met? and since the seccond?

• nancy i dont like to much your long fingers but i could house you!

• Excellent video. Your ability to write all this backwards is amazing. Well done!

• Your teach is very well my lovely teacher.

• And also thank you so much for helping us in our problem

• Where you were when i was a student? ๐ thank you very much for explaining math staff, love you โค๏ธ

• Thank you

• I luv U

• I LOVE YOU NANCY โค๏ธโฅ๏ธ from Philippines thank you for making this kind of video๐ hope your channel grow even more ๐

• this reminds me of the ood from doctor who

• where did you get the one in the numerator once you’ve integrated? 25:00

• Great presentation, but the pink marker cannot be differentiated from the whiteboard.

• By watching this video ,I only became aware of u-substitution properly

• You really made it click for me

• very clear. thank you!

• Nancy you are the best… I’m praying for you

• Perfect example of beauty with brains…..
Thank you so much Nancy. Loved your video๐

• She is “a-ight,” (for the U.S.) In Greece all women are sexy, bilingual, can teach you Calculus, cook, have style, AND will introduce you to their pretty friends, so… Nancy’s cool, but I’m not blown away.

• Nancy, you’re awesome ๐

• Nancy youre awesome your turtorials are very clearer to understand kip iTn up

• thank you very much

• Thank you so much for not being an insecure jerky math teacher!! You’re awesome.

• Thank you SOOOOO MUCH Nancy!!!!! I honestly think I wouldโve failed already had it not been for your videos! Keep up the excellent work!

• thank you so much!!!!!! your videos are so much help!

• Thank Youuuuuu!!!!!!!!!!!!!!!

• Thank you! This video not only made integration easy to understand, but it actually seems like fun. Better than any other instruction online.

• Can I download your math brain onto mine? I always wanted to do math like a genius…

• Thank you for all your helpful videos ๐

• Genius Nancy said calculus is everyones favorite lol. Greatest teacher and a comedian!

• I love the way that you teach ..
Only one cotation: sometimes you are so fast and avoid some explanations that trow me out and; thanks to the technology but also because of You ( a completelly sweetheart ) I fastforward and pay full attention I can understand …..
May God Bless you for being and have a very sweet and meak actitude with us.
I confess that in the beginning your beauty distract me so much but do not deminissed your femminity and beauty I paid more attention on every class and exercise that you solve ….
*THANK YOU SO VERY MUCH TEACHER*

• Hmmm…

• So yeah na yeah i swear i came 4 maths

• MIT grad, eh? I graduated from a school nobody outside of Colorado has heard about: MSU Denver.

• Pls come back!!! โค

• Ty

• Is 1/(2Cos^2x+c)= Sec^2/2+C?

• Thanks very much, lady! Super helpful stuff.

• Super helpful ! Thankyou โค๏ธ

• On sample no 2 can you check it i found a mistake when you try to divide the 4 / 1/2 you wrote 2 which it should be 8 and the answer must be -1/4(8)u1/2+c

• At around 14:50. No she is correct you flip the fraction 1/2 so it becomes 2 and then 1/4 times 2 = 2/4 = 1/2. The way you are thinking, distributing in the 1/4 the value of the denominator would become 4 x 1/2 = 2, which you then would flip to again equal 1/2.

• Mera logi

• thank you very much, this video was helpful!

• Took Calculus 1 two years ago and Pre-Calculus nine years before that. I’m in Calculus 2 now, and I had no idea there were such things as a “refresher course.” Needless to say I’ve been trying to re-teach myself Trigonometry/Precalculus in order to relearn Calculus 1 in order to even grasp Calculus 2. My professor has been explicitly asked twice over the past few weeks, “How do you know what to take as u?” and his answer was the same each time: “Think of it as… an art. You can’t really explain. It’s uhhh, intuitive.” (What an educator.) Sigh. These past 3 weeks have been rough. Like, really rough. Thank you for softening this hard lifeโฅ๏ธ You (and Professor Leonard) are incredible at translating this crazy conceptual language that is mathematics into sweet plain English. Thank you thank you thank youuu. My first exam is in a couple days and it’s a sweet feeling knowing I might actually pass ๐ญ

• Are you writing backwards or am i tripping?

• Where were you during my college math classes? What a great combination …. Beauty, to keep the interest up (among other things, lol!).

• Can you tech me math baby?

• Thank you Nancy for this great useful video I have a hard time understanding the math in all parts but I find your video really clear things up and very useful so thank you and keep posting these great videos

• Can solve without writing a single word.

• Math asmr

• Your very sexy

• You saved meeeeee. Thank you so much. Been struggling so much.

• you are beautiful and pretty :)…i like to see your videos

• thank you so so much! i appreciate you!

• impossible to concentrate when you are on screen!! :/

• I am a Brazilian math student. You make me like math more and more. Thank you so much.

• How you are managing your self to write mirror image so perfectly ???? Pretty impressive…

• I love you .. really

• Wow ….
I am forget study while looking u๐๐

• god damn it I’m in love

• Wait here Mr.sins is coming to help you in teaching. LOL

• Got my strong af coffee, time to study for 8 fuckin hours for my test tomorrow, lol

• Your explantions are very clear and helpful

• You taught me the thing in just 8 min which my professor took 3 classes and still I wasn’t understanding it. You are like goddess

• I really like how you provide the different “types” of problems you will see when using this process. I know you do that with all of your videos, and it’s really helpful for us to learn that, even if we are practically copying when we see it in application, but it makes it easy to catch on how it works in general later. In other words, the way you make your videos is probably the most helpful from what else I’ve seen on YouTube. Thanks!

• I love it when she says substitution… and all those other things

• Salute this lady.. She knows something that most people don’t know

• You are amazing at explaining! Thank you so much and please keep making videos! ๐

• Wow it seemed as if Nancy was feeling tortured doing the second math. My Goodness, I felt a twist in my brain and it hurt.

• Tysm for such great explanation

• Tnx this video is helping me. U r really a life saver

• Great videos nancypi!

• You the best honest

• MY GOD YOU SAVED MEE THANKKKKKK YOIUUUUUU

• Is it just me or are you guys also having trouble concentrating in the math part? This is why they say I have adhd

• hindi speak

• deepak kumar ?

• Hi qt

• You should be a web-assign tutor, all tutors over there are useless assholes.

• how I’m supposed to concentrate while she is there ?

• thank you so much for these

• you are the best

• So what you are saying Nancy is that the substitution method is the undo of Chaine Role, and by figuring out whats U is makes the process easier ?. Now the whole thing make sense to me ๐

• Thank you NancyPi! I am about to take a calculus test. You slowed everything down enough to listen to and enjoy =)

• Wow without I shouldn’t have made it ๐๐๐,,,,this was like a nightmare to me

• If I pass my mathematics course it is definitely because of this channel. You are the best

• You’re cute ๐๐

• Ahh thank you for the easy to understand tutorial! I was missing a key step for U-substitution. Now it finally makes sense!

• she has to write backwards on the glass.

• your work is very good for me so please send me some applications of intgration examples in Economics

• This is too basic

• ๐

• Thanx a lot

• Thank you Nancy. Math always plays hard to get with me. But I like it a lot. So it’s worth the โ and deep breaths and 6hr. sleep sessions.

• What if you have d pression?

• She is writing backwards

• I used to watch your videos when I was taking Algebra 1(7th grade), now I’m in 11th taking Math 130. I show your video and click immediately, thank you so much!! I understand much better now keep up the good workโฅ๏ธ.

• Can I use substitution when the problem is integral of (sqrt (x^2 + 25)) / (x) ??? I cant seem to do it someone help

• Good stuff

• Why does she always give me the vibe like she knows what sheโs doing but only from memory

• Like where the du goes that seems a little fishy

• What

• Extremely helpful! Thank you!!!

• Legend says if you watch closely, sheโs doing some math on the screen.

• Oh man, DC’s universe went so bad…
Wonder Woman had to become a math teacher ๐ฃ

• you know its a calculus video when you need reminders about adding fractions

• I kinda really love you rn

• I recommend you listen to this video in 1.25 speed

• hi nanci how are you
beautiful

maths trick

• Thank you miss Nancy!! Your teaching and explanation helped me a lot!

• How the fuck can she write backwards and solve integrations??

• Thanks Nancy pls make more vids am now a calculus nerdโฅ๏ธ๐

• Thank you for the detailed explanation.

• 2 months of calculus i still dk what in the world is it .

• I really want you to be my lecturer. Been watching your videos since 2 years ago till now. super helpful!

• Thanks mam for this video

• thank you sooooo much for making this video!!

• What if you have two terms in the integral where you’d want to substitute with u (e.g. e ^ (something) + (something else) ^2) – which one do you choose to substitute with u?

• You are an Angel of Maths. Thank you

• A tutor and a wife

• hot

• ummmmm… I love YOU.

• THANK U SO MUCH

• “U” substitution because “You substitute” and you can be abbreviated at “U”. Makes the most sense.

• Kristy Wilday ok boomer

• how come she can write backwards?

• Great video Nancy, thanks for the help!

• wow, you totally saved my life. I have a final next week and you were able to teach me what my favorite tried to teach us for weeks. !!!

• Ms please can you put up the vedio of definate Integral now

• no one explained it as you did

• For the last one would 1/2cos^2 x also be right?

• Damn ๐ฅต๐ฅต starting to like math now

• hey ๐

• could you make a video for u substitution of definite integrals?

• woow, wonderful tutorial. am grateful

• Im inlove โค๏ธโค๏ธ

• ๐

• quite helpful since you dont skip any step, even the ones normally considered trivial by others. i liked the idea with the glas plain. i am wondering how it would be if you recorded the vid not writing in mirror ways and then flip the video on the y-axis in the postproduction? sometimes it distracts that you are a cute girl, but well thats part of the show i guess ๐ anyway – good presentation with a good range of examples

• Heheh. ….i learned this in my high school only…oh by the way im indian๐

• okay

• hey Nancypi.
which app you use for this video

• If only my professor explained it like this I wouldn’t be struggling lol

• Well now you know where to come when you’re confused!

• Please make more videos about integration. Love your vids btw.

• why does du integrate to c ??

• Yoo she is realy fucking good. Made it sound so simple. And She is hot af, i would deffinatly like to be her studybudy.

• she is terrific ,,,,,

• Aise teacher mile tho ek din bhi class miss na karu

• i know it’s 2020,but still NancyPi is my girl crushh ..omg u r so amazing!!

• she’s writing backwards from her perspective??? how is she so skilled???! what!!?

• her smile and method is really beautiful <3

• THANK YOUUUUUU

• 1.25 speed bois

• to solve the integration of |x| ……plaze to day is my paper

• I keep looking at her and become unable to study

• I am getting distracted.

• i set up my eyes for 25 mins on this girl not her math

• Just wonderful

• Ok actually, this was very well explained

• We meet again Nancy.

• So perfect!

• love how you write on board its not easy

• Please make more video it really helps me

• Safe

• daym she has good backwards handwriting

• great vid

• I just can’t concentrate on her explanations because I concentrate on her face, especially her eyes.

• 5:45 Can someone explain why its (U) to the 7th power

• cuz (x^3+5 ) was raised to the 7th power and now its equal to “u” so when you put it back in, it becomes u^7

• Hussain Aladwan oh shit, thanks ๐

• nc video.it really helps me to understand.

• Please marry me

• Such wonderful explanations!! Thank you!

• Oh you are so good at explaining this! Kudos to you!!

• Beautiful

• thank you

• I do like this stuff but sometimes I can’t help but laugh at the ridiculousness of how to arrive at an answer. I wonder if the pioneers of this stuff did this on purpose…. hey Larry let’s make it like this to just see people sweat while we get a kick out of this. LOL

• Thanks Nancy for your priceless guidance. Best Wishes .John.

• This is the best thing I’ve ever watched

• You are the reason why I am going to pass Cal-II

• Hello Nancy I have this problem and I need your help: integra x^3(1+x^2)^3/2 dx . Thanks

• thank you for these videos you saved me!

• I WANT DEFINITE INTEGRALS VIDEOS!

• I was solving integration problems from my book and lost a few hemispheres of my brain and burst it into a million pieces. Thank you.

• I love your videos! They always help me so much on my exams!

• I’m going through a book right now titled Mathematics for Physicists…it discusses on Substitution of Variables (which comes from the chain rule). Is U substitution the same thing?

• learned more in 5 minutes than from a week of lecturing by my utterly worthless professor

• hey, youre pretty, i think im cute, together we could be pretty cute

• Thank you very much, I’ve learned a lot from you. ๐

• how calculate primitive of u'(x)/sqrt(1+u(x)^2) without using theorem of hyperbolique (sinhx coshx)
thank you of your help

• Gosh, she sure is beautiful. Smart, too. ๐จ๐ฆ๐นโค๏ธ

• “Why is it called U substitution? Well, no good reason as far as I know…” Classic NancyPi!!! <3

• Oh my god
Guys I’m falling ๐คค

• I really enjoyed your videos on Integrals. Great help.

• Nancypi, you’re the best teacher, I have ever found… ๐ช๐ช๐๐๐๐๐

• Best teacher ever ,your explanation is so smooth ๐ฅฐ you helped me alot

• > differential must be at the end of the integral.

but that’s just a convention isn’t it? i mean 1) i saw formulas on wikipedia that had differential at the beginning of integral sign..
2) it’s just a multiplication anyway. you multiply function by dx and integrate all of them.

• Can I Integrate you in my life ๐โค

• Thank you!

• I swear to god she has the voice of an angel

• Sexy want you

• ๐

• wish I had seen this before I failed my calc test with an 11/90 dfnjncqwlwefmoief

• THANK YOU SO MUCH

• This video replaced 3 years of high school.

• This is so awesome, the way you break things down make it so much easier to digest and actually memorize. Thanks!

• You’re amazing thank you!

• Thank you for the simplicity

• very nice and very understandable for the beginners like me.
#concise

• Hii

• Why does her integral sign look like as S

• Because the integral sign is really just a fancy S. “S” for “Sum” (of an area beneath/above a graph to the X-axis)

• I could not seem to grasp the concept of u-substitution until I watched your video. Thank you for the great explanation.

• No, I did not find “u”. But I found you

• Hi, I’m from Singapore and i just want to say that ur vids help a lot ๐

• I just realized she can write backwards ๐คฏ๐ณ

• Love you

• She is easy on the eyes

• Did u use green scree on this vid?

• thank you! i finally understand fully what to do with du!!

• Also done by the substitution 1-x^4 = u^2 , 4x^3 dx= 2u. du

• O thanku sooooo much . Your videos always help me ๐๐

• Love you.You saved my Entire semester ๐โค๏ธ๐

• U (addressing the teacher not a function) wrote everything in mirrored style (on that glass). Doesn’t this turn into a bad habit? And ur left handed.

• Or she’s right handed and writing normally and the video is mirrored

• NancyPi saved my midterm today. Thank you

• Many thanks. I have gained a deeper understanding of integration via u-substitution as a result of viewing this video.

• Nancypi I love you ……

• She is so .cute

• You guys are gross she gets so many creepy comments just because she’s a woman and does math, are you guys literally kids? Stop leaving creepy comments and do your homework

• thanks

• Thanks alot

• This legend writes everything backwards on the board so we can see it in the right direction.

• Her good thing is that she first says what is actually the subject talking about then explains it

• Ilove the way she is

• thank you very much. This was very helpful ๐

• Nancy you are super amazing. When someone is such an expert in Kenya will call him/her Fundi. Fundi Nancy! Thanks a lot!

• great video it helped alot in understanding thanks

• can you make a video on kinematics ,vectors, AP and GP

• you are a great teacher, for me . iam at harvard stem

• Support me guys๐

• Who else has watched this video because of the math

• DU believe in Love

• How can we solve the problems in case of logarithmic integration

• can u plz make a video for complexnumbers,argand digram too?

• Omg you are writing in mirror, you are so amazing ๐๐๐

• At the end u could changed that 1-x^4 power 1/2 to just square 1-x^4
Than you btw for your amazing explanations .

• Kinda new to calc here but , what happened to the square root of x plus 2 at 22:25?

• She is hot asf

• i love her.

• Oh my god. TMR is my exam and I learn integration in one video. Thank you!!!!!

• Nancy, thank you so much for saving my sorry butt again. You got me through calc 2 three years ago, and now you’re helping me review for Calc 3, Intro to Linear, and Statistics for ECE. Love your stuff – very clear, very concise, easy to understand. You might just be the only reason I get through this hellscape of a term.

• Nancy pi,you are god sent

• Thanks teacher

• Love how she’s laughing at 5:52 because she has covered the pink one from the wrong side.

• guys she’s literally writing backwards

• How Do you write backwards?

• Nancy is the whole package- smart and pretty!

• Thank uu๐ญ

• Hi Nancy

Great explanations. Can you please let me know what you are using like blackboard, please. Thanks in advance

• This was the first time I ever understood u substitution. I’ve been taught it at least 5 times but everyone else moves wayyyy too fast. Thank you for helping me out!!

• Good

• Focus on maths, not her. ๐

• My dear Nancy ooh boy. I was working on this problems all night till today. I did that way, I was working on it. I just like to listening to other people explanations that all. From other professors or professionals. I am resting my mind for some time before i finish my work. Our professor gave us 30 problems to work on it systematically. I have done half of my work. Let me just keep on listening to you attentively.outstanding explanations. Sound video to watch quietly.

• Does anyone notice that she is writing backwards this whole time?

• 25:48 u lost me there, why do we have to add the exponents if we are breaking the brackets,is it not that u*u to be power half was suppose to give us u to the power half * 2. Pls help me out Iโm lost

• Our math professor is great but due to corona we can’t go to school and he’s not explaining anything anymore, just telling us to look at the textbook and figure it out ourselves so you are literally my saviour (even tho is so weird to study maths in english lol)

• Nancy you somehow are able to make even the most complex subjects easily understandable. That is a great gift. Well done.

• Hello Nancy, I tried to teach myself college algebra and calculus.
I was not as successful as I thought, but because of your videos, I am.thanks
Your videos are excellent

• If we I do not do substitution then Integration is too hard ( time taking process ) for me.

• I had exam in 2 hours. Unfortunately, I started watching your videos and now I’ve missed my exam.

• i have a question
why is 3×2 disappears in final answer ? i thought it should have changed x3 multiply final answer ?

• i think for the second example ,it should be u ^ 3/2 not u ^ 1/2 because 1/2+ 1 is 3/2

• Too much eassy

• x2 speed is perfect

• very good videos nanci

• You are an angel from heaven, thank you so much

• Thanks again Nancy… Good mental maths and revision during quarantine. Best wishes for your health and safety. Thanks

• Very good video explaining u sub. I just have one question, may I simp?

• Love from india!! Really loved it…came to learn very easily…..best mehodology of teaching this type of complicated stuffs….which is not so now….๐

• thank you so much you really helped understand it ๐

• I”M ACTUALLY STARTING TO GET IT!

• How tf she write backwards

• I LOST KREYGASM

• Very helpful, thank you

• Nancy you are awesome at teaching! Especially during this pandemic and with online school! I hope you have calc 2 videos so I can watch those next semester!

• You are very good teacher Nancy and by the way so attractive. I love you so much

• I am confused . What should i complement : your teaching or your princess face

Well… i guess i will complement both

BTW thnx for such an amazing video

• you should be my teacher ’cause you’re so pretty.

• I love your videos. in this case however, you could have assumed (1-x^4) = u^2 . Would have made the substitution even simpler.

• I wish I could have had a babe like you for a math teacher.

• Thank you! You are very skilled and passionate with what you are doing! I hope you continue to grow and prosper (not just financially) in many different areas of your life.

• so hard to follow because i had to stare at you – pls hide your face…rly

• @NancyPi Is your camera in front of a mirror? If not do you find your self indiscriminately writing backwards in your everyday life? (I really like the idea of you honing your reverse writing technique to the determent of normal transcribing, keep it OG)

• I came for maths, I stayed for her.

• All I have to say is, Thank You!

• Thanks NancyPi. You are 50%the reason why I understand whatever I get stuck at in terms of calculus. U and Eddie woo are the saviours whenever my calculus boat is sinking

• Anyone else here for the AP tom?

• Titan Warrior Iโm dying

• Nice one Nancy. Best regards John.

• Ur so hot Nancy ๐๐๐

• Thanks soo much maa’m you made it really easy and your way of explaining is quite remarkable it was the first time when i watched your lecture but now i will follow your other lectures as well hats off to you maa’m ..,,

• i cant focus she’s so damn gorgeous omg

• Just bloody brilliant!

• Nancy, I love all of your videos. They have been very helpful to me. I hope you can make more videos. Thanks.

• Wow, you left handed and write behind transparant board, super brainiac

• Omg. So clear. How I would like to have you as my professor than my indian professor that i slightly understand him

• I really enjoyed the tutorials. Substitution made easy

• she is so cute

• you teach as beautiful as you are. love u mam pls keep up uploading videos like this

• I wanna integrate you into my life๐

• Nancy are you married? I’ve got a kindom in Africa, but we don’t know anything about integral bread. Would you like to come over to show us the truth?

• nigerian mafia, eeh ๐

• God bless you Nancy

• Thank you so much! You videos are so so so helpful! Keep it up

• I don’t know why i was smiling through the whole video looking at my screen

Not being a simp JUST a JOKE

• expontial

• how can you write in an opposite view by your left hand, you must be a math master!!

• I really understand your teachings pls keep on with the hard work I personally appreciate your efforts

• Can I integrate “u” into my life?

• Trust me if i get a teacher like u i’m never going to miss a single lecture

• Did she write it in a reverse way???๐ฒ๐ฒ๐ฑ

• Omg I love you you are the one

• Proud to be the 1000th comment!

• Thank you this really help me understand my assignment. Greatly appreciated.

• were she my lecturer, I’ll never skip a single class.

• Nancy it would be nice if you could do a video on ; Partial Differentiation
I

• Pretty Awesome

• I recommended you to so many of my friends because GOD YOUR TEACHING SKILLS ARE AMAZING

• You are beautiful and smart, you are a beautiful teacher

• First of all i wanna thanku, thanks a lot for making this video, thanks a lot for existing, thanks a lot for what I don’t know, to say thank for what ๐๐คทโโ๏ธ ??
This is the first video I have seen on your channel and this explanation is how mind blowing. But I think you are not feeling well, your voice is saying, do you ??
This is not a criticism (so please do not answer me, saying that you are one of those who criticize everyone, no matter what they do well for you), indeed I ask this question because I care about her.

• Min 7:00 Why at 8 power it is no 2 power?

• Best teacher .wow

• In India it is
t-substitution

• Thank god she’s not my teacher in school. It doesn’t matter if she is amazing at teaching, she is so pretty that I can’t concentrate!

• wait until you are 80 and you won’t care anymore

• I really like the sound of the sped up marker

• If she was my Maths teacher I’d pay attention in class 25/8

• 4:09 “Oh, You want to find me?” *WRYYYYYYYYYYY*

• Girl, you’re very good!
You should be a university professor!

• Normally math teachers look like math but @NanciPi looks like art!

• All this time Nancy has been sitting on the right side of the screen, but we get to see her mirrored side on the left … Mind Blown!

• u are my U-Substitution

• I HATE MATH COZ ITS TOO COMPLEX TO UNDERSTAND BUT HERE SHE GOES, SHE MAKES IT SIMPLE AND CLEAR. THANK YOU SO MUCH MISS NANCY!

• Idk…but she is fine asf…I’m in love…Lol…I want to learn math everyday… =D

• I would cook her the best food every day and she would never want a substitute because she would always have the real thing right beside her.

• hi nancy ๐

• thanks nancy im sleeping rn but ur lovely :DdDd

• Your work and you yourself are too beautiful.

• I would have skipped have of these steps….and that’s exactly why I could not teach to save my life

• Wow you are amazing mam.and your maths is really excellent ๐. I’m fan of your maths

• A magician and a magnet who keeps you to stay for learning. Great and a pretty teacher. Well done.

• Are you behind a glass and writing backwards for our perspective or what?

• I have spent like 3 weeks trying to decipher substitution and Alas all I needed is this video. Thank you Nancy.

• Wonderful โคโค

• ุญูุฏุฑ ูููุฏ ูุฏููู ูุง ุฎูู ุนูููู

Haider Waleed ๐๐

• Where were you when I was taking calculus? you probably weren’t born yet. ๐ It’s been 40 years since I took Calculus in college and you’ve really helped me explain stuff to my son who is taking calculus. Thank you so much!

• Such a beautiful girl!! ๐๐

• Nancy is a wizard.

• got to be the best, well paced and air tight explanation Ive ever heard. I love how she pauses and talks slowly.

• So helpful and well explained! Major thanks

• Imagine if she were writting eveything backwards; twice the difficulty, haha; btw thanks.

• Thank you.

• math gf

• Wonderful teacher

• At 15:36 there is an error ( in case people are confused) she should divide by 2 not multiply by 2.

• epic teacher

• Sham this chick doesn’t have children the gene pool is only getting worse

• U re beautiful

• I am used to watching your videos after each class to understand calc lessons. You are the best calc teacher! Thank you so much!

• I feel like she is using hypnosis to make me focus on maths

• ๐๐ is that why Iโm watching her videos even though I need the math for nothing? ๐ค๐๐คฆ๐พโโ๏ธ๐คท๐พโโ๏ธ

• You are my HERO !! <3

• You r beautiful and intelligent โค๏ธ

• So useful thanks

• Pl write in more bold figures & keep the calculation on the screen for a few seconds more.