Trig Substitution… How? (NancyPi)

Published on October 16, 2018 by

MIT grad shows how to integrate using trigonometric substitution. To skip ahead: 1) For HOW TO KNOW WHICH trig substitution to use (sin, tan, or sec), skip to 0:18. 2) For how to do a SIN SUB and WHEN TO TRY TRIG SUB, skip to 1:29. 3) For a TAN SUB with the radical in the NUMERATOR, skip to 14:41. 4) For a SEC SUB with a RATIONAL/FRACTIONAL POWER, skip to 22:36. 5) For miscellaneous types, skip to time 24:54. Trig substitution integration is a calculus technique for integrals. Nancy formerly of MathBFF explains the steps.

For my video on how to do BASIC INTEGRATION, jump to:
For my video on how to integrate using U-SUBSTITUTION, jump to:
For my video on how to do INTEGRATION BY PARTS, jump to:

Follow Nancy on Instagram:

HOW TO KNOW WHICH trig substitution to use: If the x-expression under the radical has the form of "a number minus an x^2 term", then you'll use a SINE substitution. If it has the reversed form of "an x^2 term minus a number", then you'll use a SECANT substitution. And finally, if the expression under the root is addition (the form of "an x^2 term plus a number"), you'll use a TANGENT substitution for the problem.

WHEN to use TRIG SUB: If you have an integral with a radical expression in it, and you know you cannot integrate using: a Table of Integrals integration rule, or using U-Substitution, or using the Power Rule, or using other integration techniques like Integration by Parts or Partial Fractions, then it is a good idea to try trig substitution.

HOW TO DO TRIG SUB. Here are the main steps of trig sub problems: 1) Decide which trig substitution you need [x = asin(theta), x = atan(theta), or x = asec(theta)], filling in the value for "a". 2) Simplify the radical expression by plugging in your substitution for x in the radical [For example, for a sin sub, plug in for x in sqrt(a^2-x^2)]. 3) Find dx from your x substitution. 4) Substitute into the original integral, replacing the radical, the dx, and any other x factors, with the theta expressions you found. 5) Simplify and integrate, using whatever technique you have to use. 6) After you integrate, it's still in terms of theta. So the last step is to get it all back in terms of x. Draw a right triangle off to the side, label the sides with what you know from your trig substitution expression, find the third side, and use the sides of the triangle to get an expression for whatever trig function you need in your final answer.

For more of my calculus antiderivative, indefinite integral, definite integral, and derivative math videos, as well as more examples and help with integration rules, using an integral table, integration formulas, trig integrals, completing the square, and a review of right triangle trigonometry, check out:

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  • Ꜳ I 4 years ago

    First ❤

  • Urvashi B 4 years ago

    Please make videos on solving trigonometry equation and proving identities..

  • John Smith 4 years ago

    This is my favorite Nancy outfit.

    • John Smith 4 years ago

      @Dejen Gebrezgabiher What’s the problem

    • Danana J 4 years ago

      @John Smith you own Nancy outfits?

    • Elijah 4 years ago

      Dejen Gebrezgabiher TELL US THE GODDAMN PROBLEM

    • Swapnil Iqbal 3 years ago

      @Dejen Gebrezgabiher whats the problem wtf man cant just leave us nerds hangin

    • *Floofy shibe* 2 years ago

      Dejen Gebrezgabiher it’s probably pointless to ask after a year, but what’s the problem??

  • Sal7_one 4 years ago

    Perfect timing!

  • Uriah Siner 4 years ago


    Ha! I’m a cool kid now!

  • CrazyAlaskanCoDShot 4 years ago

    Great vid 😊

  • SuperShana97 4 years ago

    I never saw this video but thank you for posting this up!
    Can you please upload the application of Integration. For example, The disk method and shell method.

  • Sanjeev Ramkissoon 4 years ago

    What If the Number That Is ‘a’ Is Not A Perfect Square For Sin Substitution?????

    • manuel zimmerschied 4 years ago

      Just keep it as a square root.

    • Sanjeev Ramkissoon 4 years ago

      Thank You

  • saleh34 4 years ago

    Easy like eating foods

  • Leonardo Camargo 4 years ago

    This is better than Netflix.

  • Tuturu 4 years ago

    I needed this like last month 🙁

  • αѕнℓєу ʝαиєℓℓєу я 4 years ago

    Coincidentally, I have my exam tomorrow morning lol. You are very helpful, thank you so much Nancy!

  • Etascope 4 years ago

    I’m replacing my x’s…trust me ^^ super great video as always

  • TheSpyfreak 4 years ago

    Hi Nancy

  • manuel zimmerschied 4 years ago

    The first time I saw this in class my head exploded. I watched the lecture again and it clicked. Thankfully we were allowed to use the formulas for the exam.

  • Peter Griffin 4 years ago

    Hey Nancy! Again awesome Vid. Would you like to concider doing a video about solving improper integrals? They are somewhat still confusing and they fit really well with your arsenal of integration and asymptote video’s!

    • netflix youtube 4 years ago

      7:50 “cluster-f*ck”

    • Mark 4 years ago


  • OrphanPaper 4 years ago

    a mathematician using the word coincidence , has the universe just inverted ,,, , that’s just evil : )
    love your word Nancy xxx

    • netflix youtube 4 years ago

      7:50 also a mathematician using the word “cluster-f*ck”

    • OrphanPaper 4 years ago

      that’s code for trig sub so is trig sub code for cluster f ,,, jusy dont watch is straight after reading that

  • Abel Lopez 4 years ago

    Awesome I love your shirt.

  • Xtra TV 4 years ago

    “I know this is a bit of a cluster-f*ck” ICONIC and SAVAGE

    • Xtra TV 4 years ago


  • Sebastian 4 years ago

    yeah, it’s intense…

  • miley ray 4 years ago

    like a math Megan Fox

    • Ejmin Ava 3 years ago


    • Beau Williams 3 years ago

      minus the surgeries and strange thumbs

    • Bo Rerun 3 years ago

      Women do think…

    • Fred Douglas 2 years ago

      Except she can actually do what she does well lol

    • Sushil Sharma 2 years ago


  • ak akk 4 years ago

    U are amazing. Thanks

  • Dejen Gebrezgabiher 4 years ago

    Very good thanks more but can you make a video about geometry please l have a lot of difficulty

  • SD Hadoken 4 years ago

    Senpai pls

  • K J 4 years ago

    You should do some ‘adult swim’ math videos with more swearing, I really enjoyed you describing the first solution as a clusterfuck

  • Jon R 4 years ago

    hey whats poppin, i got a question…how do you do them derivatives of a trig function and also how do you do those rate of change/velocity questions. Thanks homie.

    • Juice 4 years ago

      I love the comments on these videos. So unprofessional but so intelligent. Autism in it’s purest form.

    • claire li 3 years ago

      @Juice how can you just assume someone has autism?

    • Juice 3 years ago

      @claire li Because they get very triggered when you call it out.

    • claire li 3 years ago

      @Juice this guy hasn’t made a response so too quick to judge?

  • Maria das Santos 4 years ago


  • Rohan Singh 4 years ago

    I’m not a maths student

    • Parth Maheshwari 3 years ago

      Me neither but PHYSICS :c

    • Twobarpsi 2 years ago

      Or English, obviously 😂😂😂

    • MR YUP 2 years ago

      @Twobarpsi It’s ok to say maths instead of math.

    • Twobarpsi 2 years ago

      @MR YUP no

    • Some Guy 2 years ago

      @Twobarpsi they’re actually speaking better English than you

  • James Parlane 4 years ago

    I assume all of this can be used to work out the date the universe will implode on?

    • Vily Rose 4 years ago

      James Parlane at least it’d be useful 🤷‍♀️

  • Alfonso Munoz 4 years ago

    You’re right…that was intense!

  • Mandalay 4 years ago


  • Danana J 4 years ago

    7:51 excuse me? Did I hear right?

    • Jael Sonnen 3 years ago

      @PikPobedy Yeah, cuntservatards sure get worked up over the smallest things.

    • Isaac Yussuf 2 years ago

      lol a nice little laugh after finally understanding this.

    • Lauren Lofton 2 years ago

      The Mad Titan I don’t know, if you turn on the “official” captions, you get something hilarious.

    • Terence McBride 2 years ago

      I’m HOT FOR Teacher

    • Scagateher 2 years ago

      Nancy naughty lol. I had to go back to make sure I heard her correctly.

  • Graham Phillips 4 years ago

    Thanks Nancy – I always found trig subs super difficult but you explained it really clearly. You’ve definitely filled in the gaps for me – I think I’ll need a lot of practice but your video is amazing help! – thank you!

  • In_Motion96 4 years ago

    Series and Infinite Series? 🤔

  • Mark 4 years ago

    yo nancy wheres nancy merch

    • Solomon G 4 years ago

      yea we need merch NOW

  • kevin geni 4 years ago

    I love you Nancy. You are really my heroine in my time of need#calculus2

    • Muscle Gaining 3 years ago

      Dont do drugs bro

    • Ted 2 years ago


  • rhaegarbaguhin 4 years ago

    best math tutor online. we all know why.

  • Rebecca Amodeo 4 years ago

    You are my hero. Love all your videos, but I probably need this one most!

  • Jace Turner 4 years ago

    hi (sorry for bad math)

  • Robert 4 years ago

    Hey could you do a video on maximum + minimum calculus? inflection points? 🙂

  • ccsvenezuela2006 4 years ago

    Wait, I’m confused about the video. So the cops knew that internal affairs were setting them up?

  • Santiago Bron 4 years ago

    I wish you would have uploaded this video a little bit earlier.

    I just had my test on this topic.

  • Dale Kriens 4 years ago

    cluster what? that was to funny.. I think I learning something. thank you. you are a good teacher.

  • Blomoi 4 years ago

    uploaded 2 days before my quiz on this holy shit

  • Ibn Abad Alamwi 4 years ago

    i’m a good listener. that made me feel stupid.

  • vrendus522 4 years ago

    Thank you Nancy.

  • Clark Huppert 4 years ago

    You explain math very well but I am still scratching my head on this. I love the basics of trig but the deep stuff just flies way above my head.

    • manuel zimmerschied 4 years ago

      Clark Huppert it took me a second time watching the lectures to understand also just give it a go.

    • Clark Huppert 4 years ago

      @manuel zimmerschied
      Thank you Manny I will go through it again. I appreciate her style of instruction. She definitely knows her stuff.

  • Talha Akhund 4 years ago

    Can u plz solve exact and non-exact equations cuz i like the way off your teaching u have amazing skills and u r easy to understand

  • mr.rifas ahamed 4 years ago

    Thank you

  • Carlos V. Ramírez 4 years ago

    I already know how to integrate but see your videos because I love you!

  • AhBein CestCa 4 years ago

    You was in mathbff before?

  • Tyler Warburton 4 years ago

    plz have my kids

    • Tyler Warburton 4 years ago


  • Rishab M 4 years ago

    so attractive

  • Amit Kumar 4 years ago

    I love you ❤ Nancy

  • Calvin Graham 4 years ago

    thanks, so happy this is up I have a calc 2 exam this week

  • Mike Donnelly 4 years ago

    shouldn’t dx be equal to -6sinΘ ?

    • Vily Rose 4 years ago

      Mike Donnelly dx is the derivative of 6sinO (d/dx sin x = cos x ; and you keep 6 since it’s a constant)

  • Yaman Prakash Singh 4 years ago

    You are very hot

  • Adam Gow 4 years ago

    “it’s a bit of a cluster fuck” haha, love it!

  • Hoang Long Tran 4 years ago

    #calc2 please

  • orhaan d 4 years ago


  • abdu10 gt 4 years ago

    can you do polygon pls..

  • Mohammed Khaled 4 years ago

    I hope that I was the cosine ❤️

  • Camzii Matthie 4 years ago


  • Matthew Ghuneim 4 years ago

    Hey Nancy, I would love it if you did a video on series, and different tests that you use (Divergence Test, Ratio Test, etc.) to find the convergence or divergence. That’s my main struggle.

  • Mike Riley 4 years ago

    Cluster what?

  • SilentDolll 4 years ago

    Hi, Nancy! I love your videos!! I was wondering if you could do some optimization and l’hospital examples. My exam is coming up on nov 9th. D: Also, some antiderivative examples for an other video maybe? That’s our next topic after the exam.

  • patrick granier 4 years ago

    Bonjour, eest ce que vous parlez un peu le francais, Cordialement. Patrick

  • Live Ramdom 4 years ago

    Please marry me! haha You are the best TY goddess !

  • Hadeed Ahmad 4 years ago

    Nancy you aren’t making vids. Im waitin. Make a video on alevel functions plz im having trouble with that.

  • Lobsta12874 4 years ago

    To uncluster 7:53’s fuck. Use Euler’s formula [ e^ix = cos(x) + i*sin(x) and e^-ix = cos(x) – i*sin(x) ] to turn trig functions into exponentials.
    i = sqrt(-1):
    sin^2(x) = ((e^ix-e^-ix)/2i)^2= -1/4(e^2ix -2 + e^-2ix). Exponent integration just follow power rules, easy peasy.

    Eulers is like shorthand for sinusoidal functions when it comes to powers or sqrts or inverse trig functions.
    If your professor gives you a 0 because you used different techniques than they have taught 😻. If they write a one line integral that takes an 8×11 college rule sheet single spaced, to answer, bring a case of beer to the next exam and get everyone to write hollywood style gibberish on their exams.

  • Taimoor Ali Khanzada 4 years ago

    Very useful video,dear Nancy please make video on limit of sequences

  • Chris Railey 4 years ago

    Can you make a video regarding Logarithmic Differentiation and Related Rates? Please? I am currently struggling for my upcoming Calc Test.

  • Andrew Charlton 4 years ago

    I really do love you

  • Akeem Louigarde 4 years ago

    10:17 How did 36 become 18 ?

    • Akeem Louigarde 4 years ago

      shouldn’t it be (theta -(sin2theta/2)^2 +c??

  • Matt Escott 4 years ago

    liked because of the clusterfuck

  • Minju Lee 4 years ago

    Thank you so much for this video @nancypi, would you please cover improper integrals asap?

  • Monkey Monkey 4 years ago

    ~7:41 hmm. I would have loved to have seen your notebooks when you were in school. Regardless that it is obvious that you can derive what you need… you also have a shitload of identities tucked up in them brains. Who would have known that multiplying by one would be so important!?!!

  • Stacy Yardley 4 years ago

    I just watch couse your hot

  • Sunny shah 4 years ago

    Did she just say “cluster-fuck”
    i’ve never heard her use a cuss word before.

    • TheUndisputedAngel 3 years ago

      If you turn on captions, (not the auto generated one) is says she cursed

    • Daniel Choi 3 years ago

      I thought she said “this is a little bit of a cluster but…”

    • Harry Ross 2 years ago

      It was at 7:55 and she’s right.

    • Jake Keith 2 years ago

      That’s what trig sub’ll do to a person.

    • Clifford Williams 2 years ago

      OH my gosh NANCY!

  • ananto elahi 4 years ago

    I don’t know if the student teacher policy exists through youtube. PLEASE GO OUT WITH ME! one date.

  • ananto elahi 4 years ago

    LOVE your work.

  • Kevin Poulet 4 years ago

    Can you do a video on integrals by partial fractions or integrals using double integration by parts

  • Barış Akyüz 4 years ago

    nancy will you marry me???

  • Ezequiel Torres Lagunas 4 years ago

    Awesome!! I get it, YOU TEACH VERY NICE.

  • Ezequiel Torres Lagunas 4 years ago

    The steps you use are ordered and with a lovely touch

  • Ezequiel Torres Lagunas 4 years ago

    I love The Trig and I like you too.

  • Kevin Maldonado 4 years ago

    Can you please do some topics that’s going to be on Calc 2 and Calc 3

  • roger okon 4 years ago

    you ever want a hot math teacher. well this is her

  • M77 Mo 4 years ago

    you are realy feel us 😍

  • Gerry Wong 4 years ago

    Can you do a video on Riemann Sum ?

  • Jelly Jams 4 years ago

    Your voice and energy are so damn comforting. Are you like 27 years old ? You have a master is mathematics ?

  • Leo Mulder 4 years ago

    Hi nancy! Do you have any episodes on Taylor series?

  • GOOFY 4 years ago

    I’m not even in this class yet. Rip

  • Jennifer Jane 4 years ago

    Nancy i love you

  • Gaby P 4 years ago

    Can you make more calculus videos 🙏🏼 past derivatives & implicit differentiation. Such as related rates? Or derivatives of inverse functions?

    • Run trunks 3 years ago

      Yes, please.

    • kumar upendra 2 years ago

      watch my video for all types of Differentiation Problems

    • Navjot Singh 2 years ago

      kumar upendra it says your channel has no videos …….

  • hehehe 4 years ago

    Areas and Integration pleaseeee thanks!

  • Hadeed Ahmad 4 years ago

    I am still waiting. Plz make a video on cie alevel functions topic.

  • Nitte Molta 4 years ago

    Your are my good tutor Nancy. More grease to your elbow…

  • Gautam Verma 4 years ago

    *She is a complete pack.*

  • Gautam Verma 4 years ago

    *I can’t handle such intense classes*

    • Anuq Nalawangsa 2 years ago

      Get a room…
      For yourself.

  • Sam Fraley 4 years ago

    Could you do one on partial fraction decomp?

  • Black bones 4 years ago

    You are so beautiful then how can I concentrate on question 😘😘

  • Molalign Alemnesh 4 years ago

    you talking a lot ,

  • PESHAWA sdiq 4 years ago

    Please result of here what is?
    lim 1-cos3x/x^2

  • Sian Gu 4 years ago

    Thank you so much. You are the best math teacher I found online.

  • Sian Gu 4 years ago

    If you have time, could you make some video about probability? Thank you so much

  • Maka Infinity 4 years ago

    Question where can we ask you math question? Like how and when to do the chain rule with product rule.
    Thank you love your videos!!

    • MATH With Iskender 4 years ago
  • MATH With Iskender 4 years ago

    follow me 🙌

  • Kathy Reyes Hernandez 4 years ago

    16:03 “Some people use ‘you’ “ 😢 lol

    • Keith Perry 2 years ago

      Haha yes that was funny!

  • mjs28s 4 years ago

    question – even when you can use more than one method to solve problems (trig sub, u/v sub, etc.) would it be better to just master trig sub and to use it even when you can use other methods (at least until you master it)? My thinking is that if you have trig sub down like an old habit you won’t get thrown for a loop when you get a problem that requires it. If you have it mastered, then learn the easier methods. Past experience with other math course is that sometimes we get used to just solving the problems quick and clean then when we need a more complex method that we haven’t practiced….screwed.

    It is a bit brute-force for awhile. What are your thoughts?

  • simplytanya 4 years ago

    ah Nancy your videos are so great! saving me in calc bc

  • Harrison Walls 4 years ago

    Shes so pretty

  • AIMBOT 4 years ago

    I had so much fun watching this Nancy chick 😛💗

  • Someone✈️🥀 4 years ago

    well, you are skipping a lot of steps i cant understand 17:40

  • Caleb Frank 4 years ago

    Before I watch your videos , I like them first

  • Rajendra Misir 4 years ago

    Excellent explanation of this technique using good examples. Very helpful and insightful for me. Thanks Nancy!

  • Joanna Wuko 4 years ago

    love of my life

  • Shahanie Baguinsodon 4 years ago

    Can you make more integral calculus videos

  • A.shakur Ahmed 4 years ago

    Exactly I love you although I don’t know where are you …..

  • Sherry Liu 4 years ago

    Thanks Nancy! Saved me right before finals :’)

  • hey there pretty brown eyes 4 years ago

    this stupid shit is driving me insane, wouldn’t wish this upon my worst enemy

  • Aman Official 4 years ago

    great teaching. .. Nancy I love you … plz contact me Whatsapp +923369769880

  • turtlehater2 4 years ago

    “I’ll be right by your side….”Prof during final: “Who is this?”

    • Noah Gracias 3 years ago

      seems legit

    • Patrick Bossome 3 years ago

      C’mon it’s Nancy! Everybody knows Nancy

    • Jon Bilbao Mallona 3 years ago

      @Patrick Bossome Is it true that she was born in a cherokee tribe and was kidnaped by a pastor at the age of 3?

    • Jeremiah Carr 3 years ago

      I would mess my trousers if this girl was even five feet infront of me she is so dreamy

    • YoshiCookiesZDX 2 years ago

      @Jeremiah Carr Yikes…

  • turtlehater2 4 years ago

    when im doing my homework and trying to write stuff down quickly i make the little whizzing noise like in ur videos when you write stuff down

  • A M S 4 years ago

    You’re amazing Nancy how you write mirror image with left hand 🙂 Did that take a lot of practice? I’d love to see a video on how you do that.

    And your math tutorials are the best! Especially the more complicated ones. Just the right depth for practice. Keep up the great work!

    • Legendary Sam 4 years ago

      A M Salim she writes is normally and mirrors the video. If she didn’t mirror the video we’d be seeing/reading it backwards.

  • bicboi46 4 years ago

    Its really cringey seeing these thirsty people comment on nancys looks. Get over it, relax.

    • Louis Hennick 3 years ago

      Brandon Brea exactly I was thinking I’m in high school and doing this and I’m nothing special yet this guy is reviewing trig sub for engineering?

    • Jacob yt 2 years ago

      @Username HAHA, well said, regarding @alb12345672.

    • Vaiebhav Patil 2 years ago

      U GAY

    • Grace M. 2 years ago

      literally. like she’s just doing her job.

    • Ken Meyer 2 years ago

      probably all from muslim countries where women are outlawed.

  • feilong 4 years ago

    Nancy for president👆

  • Seth Macomber 4 years ago

    Oh awesome! This helped me a ton. Thank you!!!!!!! P.S. you totally won me over at 7:51 lol

  • Maclean Gondwe 4 years ago

    you the best…i like that girls prove to guys wrong… that girls can also do better than boys

  • Meteor2997 4 years ago

    Кто дрочит на это? Ставь лайк))

  • Jason Jackson 4 years ago

    I hated trig substitution back in college. This is worse than I remembered. I can’t believe I made through calc 2.

  • dik2bik 4 years ago

    Clusterfuck indeed

  • Emin B. 4 years ago

    how can you write like that? Are super genius like 200 IQ???

  • Doc Moore 4 years ago

    Nancy almost seems to have elastic arms. Look at how far that girl can reach. I think the writing backwards part must be a software trick, although, I had one professor who could write with both hands at the same time, both sides of the equations went up at the same time with the result that NO ONE IN THE CLASS could ever keep up.
    Thanks Nancy…You make it all much more interesting, and thank you for the candor…YES, we all use tables whenever we can. I’ve lugged Abramowitz and Stegun into more than one open book final exam.

  • Mark Zamani 3 years ago

    Hello! at 7:22 why can’t you rewrite sin^2 theta as (1-cos^2theta) and just use U sub? If anyone can explain i’d really appreciate it thanks!

  • Soufyan Lamrini 3 years ago

    20:45 can someone explain what happened?

    • Dream-Catcher 3 years ago


  • RIZVI rizvi 3 years ago

    You are Soo beautiful

  • Daniel Afifi 3 years ago

    you beautiful we should hang out together miss

    • GreenParrot77 3 years ago

      no shes mine

  • Jayyy Zeee 3 years ago

    @NancyPi, I like your sarcasm at 5:37. Thank you for these videos. I learned these things many years ago, so this is a refresher for me. I have no purpose for it other than pure interest. Yours are my favorite. I like the pacing and format. You’re also extremely easy on the eyes 😉

  • Michael Macdonald 3 years ago

    She is quite excellent writing backwards. Also try Paul Dawkins calc notes.

  • Ghufran Khan 3 years ago

    Hii nancy…

  • Ghufran Khan 3 years ago

    Complete pack…

  • Badruddin Shaikh 3 years ago

    Thank you so much……. God bless you mem

  • MarkTheShark 3 years ago


  • Joe Dempsey, Sr. 3 years ago

    Good explanation. You had me at “clusterfuck”. 😉

  • MrBat000 3 years ago

    Are you a school teacher by any chance?

  • Mak Edward 3 years ago

    For the sec sub, as the radical is the denominator, should we consider the domain of the integrand?
    What if multiplying x with the radical?

  • Charles MC 3 years ago

    At 2:12 that integral can be done by partial fractions (no need for inverse hyperbolic trig functions there).

  • Lightworks Tutorials 3 years ago

    is it only me that is amazed that she can write backwards??

  • Ryan Metevier 3 years ago

    Your saving my life and my degree 😂

  • Jon Richards 3 years ago

    integration makes me wanna kill my self

  • Liang Zhang 3 years ago

    What a legend! Thank you for helping

  • BASEsick TRUTH 3 years ago

    You are a perfect 10 out of 7

  • LeadingThePack 3 years ago

    Liked just for 7:51 because that’s how I’m feeling after getting a 68 on my first calc 2 exam.

    • Coxy Normus 3 years ago

      Bet the class avg was a 40. So good job! You’ll make it. Trust the curve (if your prof is nice enough to appoint one!)

  • kray97 3 years ago

    Basically you are changing the basis of integration from x to theta. This is a lot easier to explain if you use the triangle to explain it first, and then show it in practice.

  • Jagruk Janta 3 years ago

    Nancy I lv u….

  • Luper 3 years ago

    I can legit focus on this video really well. My prof has a greek accent so it’s sometimes hard to hear and pay attention to what he’s saying but this is really really great! Thanks for the upload Nancy!

  • Noah Oller Smith 3 years ago

    Great video and effective way of explaining it.

  • Bhavya Chheda 3 years ago

    Keep on making maths videos….you will help a lot in increasing worlds average IQ

  • Saman Afrooz 3 years ago

    In first example sin substitution the finale answer I think instead of x/2 should be x/36 because 6×6 is equal to 36 thank you so mush 🙏❤

    • Saman Afrooz 3 years ago

      Oh I realize you make 36÷18 and equal to 2 tnx for your help 🙏❤

  • Rose 3 years ago

    Partial Fraction Integration keeps tricking me up, any suggestions?

  • Yeabsira Getahun 3 years ago

    whenever you say “Okay, let me help you out.”, my spidey sense tells me I’m not going to understand what you are about to write

  • Valentine Liona 3 years ago

    u r great …i lyk ua teaching

  • mahendra singh 3 years ago


  • steven morty 3 years ago

    i didnt even see what she was writing

  • Jean Algarin 3 years ago

    I dont know how i end up here but i dont regret😍

  • J C 3 years ago

    I’m sorry…There was calculus in this video?

  • abdul latif 3 years ago

    Nancy you made calculus 1 easy for me… now i am taking cal 2.. and i have no clue how to do it without you… please make it soon

  • mrchapsnap 3 years ago

    When she says “don’t be scared of the trig,” it sounds like she’s saying it to herself as much as she’s saying it to us…

  • Coxy Normus 3 years ago

    Thank god you wrote the rules, I was not prepared to research those and my professor didn’t show my class like 50% of them -_-

  • Lego Play Time 3 years ago

    15:00 You can actually do it without trig sub.
    Rewrite it as root(25+4/x^2)/x^3
    Essentially moving an x term from the denominator into the root.
    Now, let the part inside the root equal to u.
    On differentiating u, we get -8/x^3
    Multiply and divide the integral by -8
    Solve the rest using u substitution

  • CEAS Email 3 years ago

    Vector calculus….please…. -_-

  • Jordan Benzoni 3 years ago


  • Hassan Omran 3 years ago

    Sexy lovely beautiful and professional tutor 🌹🌹🌹🌹🌹♥️♥️♥️♥️

  • General Kenobi 3 years ago

    Not to be weird, but she is pretty. Don’t even @ me.

  • glorymanheretosleep 3 years ago

    At 13:19 where did the – (x/2) come from?

    • Daniel H 3 years ago

      cus sin(θ) = x/6 and cos(θ) = sqrt(36-x^2)/6
      you have 18*(θ-sinθ*cosθ),
      multiplying 18*(-sinθ*cosθ) =
      or (18/36)*(-x)*(sqrt(36-x^2)) and 18/36=1/2
      so (-x/2)*(sqrt(36-x^2))

  • DragonPnoy88 3 years ago

    Charlie Foxtrot

  • The everything Channel 3 years ago

    for god sake please stop smilling!!!
    your smile is killing me!!!!!!
    I cant concentrate !!!!
    someone pls help!!!

  • Chris Davison 3 years ago

    Hey Nancy, You made a mistake. at 14:37, your final answer has an x/2 where an x/6 should be. I think, that is if sin(theta)=x/6.

    • Robert Stone 3 years ago

      I thought the same thing. Wouldn’t the sqrt(36-x^2) also be /6 if cos(theta) = sqrt(36-x^2)/6.

    • eman297 361 3 years ago

      @Robert Stone 36/18 =2

  • TheFenerbahceSK 3 years ago

    Do you make calc II vids?

  • MrVoayer 3 years ago

    OK ! Let’s be honest: Trig substitution is a difficult stuff. There are a lot of rules, a lot formulas to know by heart, a lot of tinkering around…
    But you certainly did a great job in covering a lot of it in a really understandable and helpful manner.
    This video should be seen several times until it is all sinks in !

  • Emmanuel Nava 3 years ago

    I threw her a like the moment she said “clusterfuck”. Amazing

  • Luis Medina 3 years ago

    Im more impressed on how you can do this writing backwards!

    • Vres 3 years ago

      She doesn’t. She uses a simple trick but wants it to be a secret

  • Hayder Al-Lami 3 years ago

    Nancy, you did a great job

  • Abhishek Adhikary 3 years ago

    You are very beautiful

  • Abhishek Adhikary 3 years ago

    Your class is also effective

  • Abhishek Adhikary 3 years ago

    Nice class

  • balu Rathod 3 years ago

    Great job nancy .love you from india

  • Sad story 3 years ago

    Where r you from?

  • Sad story 3 years ago

    I want follow you directly

  • Programmingnoob 3 years ago

    Theres always a big inhale with nancy videos xD

  • Omar Hammami 3 years ago

    nancy pi deepfake in the works

  • Glenn Rickelton 3 years ago

    How did you get 125/ 4 in example 2 at the 18 minute point?

    • Marie 3 years ago

      right? I cant figure that out

    • Marie 3 years ago

      wait! I got it!

      ok so on the denominator you see the term (2/5*tantheta)^4 right?

      So take (2/5)^4 and you will get 16/625, so because this is in the denominator to flip it to multiply wiht the 2/1 and 2/5 term you flip it to be 625/16.

      now simplify (2/1)(2/5)(625/16) = 2500/80, simplify this by a factor of 20 and get 125/4

      Hope that helps!

  • Cups Edits 3 years ago

    I would never miss your class if you were my teacher😍

  • Cups Edits 3 years ago

    You look like my crush😍🔥🔥

  • Elias Zacarias 3 years ago

    Trig substitution was definitely the trickiest thing for me. With your explanations however it all makes sense. You are a superb teacher. Thanks.

  • Usha R 3 years ago

    Very informative thnx!

  • Chao L 3 years ago

    You explain so well! Thank you!

  • Ahmed Zaki 3 years ago

    How she write on the board?!

  • Lay 3 years ago

    20:47 can someone please explain to me what happened here? i am lost huhuhu

    • MR YUP 2 years ago

      u = sinΦ
      you will then use the power rule to help integrate 1/u^4

  • James Swims 3 years ago

    A beautiful woman who describes a grouping of trig integrals as a clusterfuck has a very bright future in teaching! I, for one, will forever be your disciple.

  • Rahmat Abadi 3 years ago

    Please teach me the proof of Fermat Last Theorem.

  • Zamran Ali 3 years ago

    5:37 Nerd Alert !

  • Daniel Santos 3 years ago

    i love you

  • Your Channel 3 years ago

    *I wish this would have happened **0:13*
    *You were by my side.* 😍

  • Cooper Osgood 3 years ago

    Why is the denominator of the last problem just a normal square root instead cubed square root?

  • Ilias Kaykobad 3 years ago

    Your mesmerizing look causes distraction in my concentration towards math..😆😆😆😆

  • Soren P 3 years ago

    Oh my hru nancy? Fancy Nancy 1+1= 3;) if u n me

  • Rojeh 3 years ago

    And I thought Chinese was a hard language.

  • Paul Garcia 3 years ago

    I had to turn on captions to confirm what I heard at 7:50

  • Nate Mac 3 years ago

    I suddenly enjoy trig sub integrals.

  • Jake Lopez 3 years ago

    Haven’t seen anyone mention it, but I love that background hum when you speed up your videos.

    • Danny DarkSide 2 years ago

      That sound is strangely satisfying. Lol

    • Arthur Callaghan 2 years ago

      Me too!!!!

  • Jake Lopez 3 years ago

    Nancy doesn’t seem to like trig.

  • yourfavoriteweapon92 3 years ago

    thank you thank you thank you thank you thank you thank you thank you thank you

  • Nik Kolar 3 years ago

    Question here, why do you replace x with theta in dx at 6:05. I know you got to rewrite everything in order to be in terms of theta I just do not understand how you have got this expression 6cosΘdΘ, especially dΘ at the end 6cosΘ is x that I know.

    I understand everything else perfectly though, outstanding lessons thank you Very Very much Nancy world needs more people of your kind!❤️🤓

  • Gabriel Ramirez 3 years ago

    You already have written that 6cosø = sqrt(36-x^2) so you dont need the triangle to figure out cosø = sqrt(36-x^2)/6 just saying

  • Paulo R Menezes 3 years ago

    Nancy is, by far, the prettiest and hottest teacher ever.

  • gentlemandude1 3 years ago

    20:54 “Use the power rule to integrate…” I’m not sure what you mean here. Wouldn’t u-substitution be more effective?

    • MR YUP 2 years ago

      it’s a u-sub then the power rule. She skipped the steps.

    • gentlemandude1 2 years ago

      Got it. Thanks!

  • SHIVAM BEN 3 years ago

    Why se use trignometric function in integration , madam specify extensively.

  • teddysurf 3 years ago

    There is never ever been a cool kid that has said “trig sub”…

    • Samuel Feaster 3 years ago

      teddysurf Yes there has been. She just did it.

    • teddysurf 3 years ago

      Samuel Feaster lol

  • Habqaad Media 3 years ago

    Pls stop more talking I cant wait the calculation

  • tahir rizvi 3 years ago

    Can you use trigonometric substitution to differentiate?

  • Sam Pitts 3 years ago

    I have my second wind this is a cool class 👌😎 thanks 😊

  • Laercio Civali 3 years ago

    Please how to integrate (a/1-a)^5/4 da ?

  • Johan Fasth 3 years ago

    I thought I was quite decent in math. Nope, apparently not… Didn’t got anything of what she said… 🙁

  • Klingende Mynt 3 years ago

    Had to watch some of these videos on VLC, flip the image horizontally. My god! Nancy is drop dead gorgeous.

  • Hamza Abbas Zaidi 3 years ago

    Can you use trig sub to differentiate?

  • kushal neupane 3 years ago

    I Lost my concentration. Why??

  • Jena Shiblak 3 years ago

    your videos help so much! can you make a video on Application of integration to Arc Length and area, approximate integration and improper integrals?? Thank you so much for all you do!

  • Victor Bezak 3 years ago

    I love math, and I’ll have all of this down pretty soon. But at first exposure… it’s kind of insane how wild solving these problems is getting lol

  • Birson Engleng 3 years ago

    mam can you please make a vedio of method of substitution!!!!please mam

  • FOREVER EL1TE 3 years ago

    I don’t understand how square root of 36-x^2 changes into 6cos of theta, can someone explain

  • Ram ji Patel 3 years ago


  • Yashashree Pawar 3 years ago

    Can you explain me
    How can we decided..what can be considered as ‘ t ‘ out of numerator or dinominator in case of integration by substitution method of integration
    Please do replay

  • Cre4ture 3 years ago

    This is the most random recommend video I’ve ever gotten. I haven’t had to do this since freshman year and I don’t plan on doing it this year or my senior year.

  • James Lindgaard 3 years ago

    Any idea where we can find some practice problems?

  • Eduardo Garcia 3 years ago

    This really helped my out on my test. Thanks Megan Fox, very cool!

  • Asa Tshazibana 3 years ago

    i heard to replay 7:51 like 20 times and the closed captions confirmed it.

  • Grant 3 years ago

    “This is, a bit of a clusterfuck. This is more than you would ever ask for.” THANK YOU! SOMEONE SAID IT!

  • A.A .Y 3 years ago

    You should do more

  • Blockanese 3 years ago

    I feel like my tuition money would go to better use to you than my math teacher.

  • Zimpan zee 3 years ago

    0:38 when you fall in love with your student which he is actually a cool guy in class

  • Andrew Huss 3 years ago


  • amzar asri 3 years ago

    I dont understand at all.
    Poor me.😕

  • Rami Yako 3 years ago


  • Terra Florim 3 years ago

    Will you ever do partial fractions?

  • Jaziel van persie 3 years ago

    Isn’t it suppose to be 125/8 not 125/4?

  • Phu Q 3 years ago

    I wonder if she realizes how pretty she is.

  • Mr Nightmare 3 years ago

    you are a life saver for me. Thanks a lot 🙂

  • Manav Naik 3 years ago

    Dude is it just me or is it impressive she can write in mirror reverse. Seriously though channels like yours make math seem simple for everyone 😀

    • Praveen Saravanan 3 years ago

      You do realize people don’t actually do that right?, Its pretty obvious considering you’re smart enough to learn integration.

  • bruce slasher 3 years ago

    Like ur top or what it’s called

  • AdnaNandA 3 years ago

    Wish me best of luck guys. It’s midnight now & tomorrow is my exam. But here I am binge watching her tutorials which are not related to my exam topics at all.

  • Severed Magic 3 years ago

    I was struggling with this section. Thanks

  • Andrea Leandro 3 years ago

    “I know I love finding new integration techniques in my free time” giiiiirl in need that brain ♥️

  • Neil Anderson 3 years ago

    Pls post a video proving that the trig substitution gets the right answer.

  • ford fairlane 3 years ago

    1+1=2 lol

  • lombaxjcd 3 years ago

    c l u s t e r f u c k

  • Jake Rabbets 3 years ago

    Is she left or right handed?

  • knowledge boy 3 years ago

    20:49 how to integrate that?

    • MR YUP 2 years ago

      u-sub then power rule

  • CommanderGabby 3 years ago

    NancyPi notice me crush,plss

  • Ryan Sleek 3 years ago

    thanks nancy!

  • Y/J/BTS 3 years ago

    “replace those x’s and clean it up” hmmmmmmm

  • Jomz 3 years ago

    The integral of cluster fuck is

    fuck yeah.

  • Andrew Nield 3 years ago

    you make me want to watch math videos

  • James Vlasis 3 years ago

    Pause at 7:52 and her look sums trig sub up pretty well 🙂

  • Ghost Town 3 years ago

    I don’t even have maths as a subject…but im interested now 😁

  • Matheus Nambahu 2 years ago

    I skip this shit in the exam

  • Umer Mehtab 2 years ago

    Hi I love you
    Will you marry me I am 18years old

  • كفاءة I KAFAAH 2 years ago

    Teacher Nancy could you make a video without appearing on it ? Because all the video I was focusing on you instead of the explanation , you are so cute !!

  • l kern 2 years ago


  • usman saeed 2 years ago

    Nancy you are looking cool in this dress

  • lucy laurian 2 years ago

    you are great woman i salute you. thanks for all your videos

  • John Vandersall 2 years ago

    sugar britches what can we do with this

  • Clifford Williams 2 years ago

    “Don’t worry! I’ll be right by your side.” Awww, Nancy!

  • Kaihii Aleshiikho 2 years ago

    Come to India,………….

  • Anas Salisu Ali 2 years ago

    Need more example

  • Clifford Williams 2 years ago

    @1:50 Nancy compliments your intelligence!!!!

  • Clifford Williams 2 years ago

    There _has to be a better way to get sardines out of a can

  • Paul Price 2 years ago

    My god your so attractive. Wtf. Stop it just stop it already your killin me over here.🤔🤔🌹🌹🌹

  • Yohan Afewerki 2 years ago

    wait, is her writing backwards???

  • Jossi Ossa 2 years ago

    I will like private lessons when i am alone at home…

    • MR YUP 2 years ago

      Sure, private online

  • Carlton Fogle 2 years ago

    I feel lost knowing that this is as far as Nancy takes us into calculus 😭 thank you Nancy!

  • SantaFeScout 2 years ago

    Love watching her videos, whatever it is she’s trying to explain I don’t understand. It just makes me concentrate more on delivery

  • Andy Tachiki 2 years ago

    at 17:40 wouldn’t the sqrt[(2tantheta)^2+4] be equal to sqrt[(2tantheta)^2+2]? I don’t understand how she got what she had there.

  • Brendon Patterson 2 years ago

    @7:50 when you’re not used to Nancy cursing D:

  • gunsboy77 2 years ago

    Very informative but Closed Caption action wrote cluster-f… lol

  • wisam alkhoory 2 years ago

    why dont u just draw a triangle and make your life easier

  • Tim Tran 2 years ago

    Thanks Good

  • Caye Zara 2 years ago

    Beautiful and gorgeous Nancy.

  • Jimaale jillow 2 years ago

    Can I have your contact plz

  • Eric Mckinney 2 years ago

    Awesome video Nancy! Way to send it on trig substitution. I am cruising through Calc II thanks to your videos. Keep up the great work!

  • Japheth Canales 2 years ago

    I fall in love

  • MS Animations 2 years ago

    It’s a really awesome …..thank you Nancy

  • Terence McBride 2 years ago

    I wish my calculus professor was that gorgeous
    my teacher looked like a homeless santa claus…
    and he was not very jolly around midterms and the final exam

  • Khushank Verma 2 years ago

    I have another Method for integration{( x^2)/ root(a^2-x^2)}dx
    We can subsitude sin(u)a=root(a^2-x^2)

    • Khushank Verma 2 years ago

      You will left with(cosu) ^2

  • Keith Perry 2 years ago

    Awesome tutorial. She just explains what it is. Where were videos like this when I was a math student? Why didn’t my professors just explain it this simply?

  • Shafe 2 years ago

    so I started saying words like *trig-sub* , *u-sub* , guess who’s the coolest guy in the school now

  • Rakshit Bhoj 2 years ago

    was searching for this top like hell thnx alot ma’am

  • Paola Karime Meza 2 years ago

    Hello, I am having trouble understanding how she got (cos θ) / (sin^4 θ) 20:45
    Could someone explain it please?  😥

    • MR YUP 2 years ago

      u = sinΦ
      you will then use the power rule to help integrate

    • Paola Karime Meza 2 years ago

      MR YUP Thanks! 😁

  • MetaStag 2 years ago

    Can you make a video on How to to add numbers?

  • Putra Habirun 2 years ago


  • Rebecca Luo 2 years ago

    bless ur soul

  • 天沢聖司 2 years ago

    Wow. Ur my idol. You just saved me for my midterm. Greatly appreciate it.

  • Flash Gaming 2 years ago

    Ma’am lovve you

  • Flash Gaming 2 years ago

    And your explanation

  • Rodrigo Gomes 2 years ago


  • Keter Cubas 2 years ago

    have you thought about how many engineers you’ve molded?

  • AnselAlly 2 years ago

    I gave up around 7:21 maybe math is a 2-semester course.

  • Brian.K 2 years ago

    She rights in mirror but still have a better handwriting than me

  • MR YUP 2 years ago

    11:30 To solve for cosine why can’t we just divide both sides by 6 and get the same answer we got using the right triangle trick?

  • Roshan John 2 years ago

    i love you

  • bradley booth 2 years ago

    Got damn, there’s sooo many steps that you get lost along the way arrrrgghhh. I gotta practice some more because I felt like I got left behind since from the jump.

  • Injamul Haque 2 years ago

    You are great mam

  • Arnav Jaydev 2 years ago

    She’s smiling a lot.
    She might have met someone….

    Just saying

  • Juan Garcia 2 years ago

    Me gusta como explica, pero me perdí en su mirada

  • glorymanheretosleep 2 years ago

    Would you like to have my children? Nancy, you need to do more challenging problems.

  • Matt Brown 2 years ago

    How the hell do you ace calculus 2 when it’s this hard?

  • roland montemor 2 years ago

    It helps so much. Thank u Nancy 💓

  • Good Vibes 2 years ago

    All of a sudden I have an overpowering urge to watch math videos! Please marry me 💐💐🥰🥰

  • yufaihong 2 years ago

    Not that easy.

  • Malignus Von BotterShnike 2 years ago

    I think imma just do engineering at university so that I have an excuse to assume sin(x) = x every time

  • Nujcharee Haswell 2 years ago

    How did we know dx is 6 cos theta d theta at 6:46 please?

  • Karam Productions 2 years ago

    Are u phd??? :))) Marry me plzzzzzzzzzzzz

    • Karam Productions 2 years ago

      aai am luukeeng phor braeed

  • Johan 2 years ago

    Thank you 🙂

  • Safwan Al Islam 2 years ago

    never expected her to curse but okayyy professor. You naughty naughty!!!!!!

  • Raymond Rodgers 2 years ago

    We maza unajua sio poa🤕🤔

  • Ethen joe's 2 years ago

    Could u mind clearing my doubt:-
    My question is at the time stance 24:30,how did 64|tan|cube turn into tan square theta??

    • Anthoni Flores 2 years ago

      This link: you’ll find answer to your question friend.

Comments are closed.