Integrate 1/(1+x^3)

[@TonyTheShooter]

I love how clean you are to teach!

[@basil-vander-elst]

Yeah and his hand writing is very beautiful

[@toymurotjorayev8571]

Yes ser

[@benheideveld4617]

Excellent teaching also beautiful blackboard writing looking at the camera ads a nice personal touch Finally nice voice and good english without strong regional accent

[@elquesohombre9931]

I’m always a fan of accents for whatever reason…

[@benheideveld4617]

@@elquesohombre9931 That is because RP comes across as arrogant. Most liked English accent is Australian, however there are quite a few Australian accents…

[@holyshit922]

1. Basic infoormation about real numbers 2. Basic infoormation about functions (including one to one function, composition of the function, inverse function) 3. Sequences 4. Limits including continous functions, asymptotes 5. Series (limit of sequence of partial sums) Necessary condition for convergence comparison test, ratio test, root test 6. Derivatives Limit of difference quotient Basic differentiation rules like linearity, product rule,quotient rule,chain rule, derivative of an inverse function slope of tangent line, increasing, decreasing functions, extrema, inflection point,concavity L'Hopital's rule Taylor and MacLaurin series 7. Indefinite integrals Riemann sums Basic integrating techniques like linearity of integral, integration by parts, integration by change of variable Integrating of certain class of functions like rational functions 8. Definite integrals Newton - Leibniz theorem, techniques for integration definite integrals Applications of the integrals (area under curve, length of curve on interval , volume of revolution surface area of revolution) Improper integrals 9. Maybe something on multivariable calculus 10. Differential equations You have series on linear algebra Maybe series of videos about these topics

[@PrimeNewtons]

Thanks . I love your suggestions. I need to reset.

[@holyshit922]

@@PrimeNewtons In your algrebra series only orthogonalization is the topic I would like to see which includes 1. Rotation matrices 2. Reflection matrices 3. Gram - Schmidt orthogonalization process 4. QR and QL decompositions 5. Orthogonalization of polynomial basis with certain inner products f.e. inner product \int_{-1}^{1}p(x)q(x)\cdot\frac{1}{1-x^2}dx gives us Chebyshov polynomial (I know that your transcription of this name is Chebyshev but Chebyshov is closer to the original) inner product \int_{-1}^{1}p(x)q(x)dx gives us Legendre polynomials inner product \int_{-\infty}^{\infty}p(x)q(x)e^{-x^2}dx gives us Hermite polynomials inner product \int_{0}^{\infty}p(x)q(x)e^{-x}dx gives us Laguerre polynomials Next series could be series for analysis I am not a teacher and list of topics for analysis could be modified but in my opinion series of analysis videos should contain these topics First two topics on my list are needed for introduction to mathematical analysis When i was younger I would like to become a teacher of math and physics but I didn't make it

[@AZ-by5ps]

Thank you very much for sharing. Now I'm 54 years old. By watching your video, remind me how I solved Intergeral questions 40 years ago. This is one of my foverite topics in mathematic.

[@paulgillespie542]

Nice catch of your distribution sign error. It shows that you quickly review previous steps for this kind of error before proceeding. I can't tell you how much time this quick check has saved me. No need to edit the video: this is a teaching moment on its own. Well done Professor.

[@Woobbled]

Hello sir. Your videos are amazing. Last night at 1 am i rewatched your video on integrals. Not only are you a good teacher but your enthusiasm for the topics you teach have made it much easier to learn and comprehend. Just now i saw your video and almost shed a tear at the fact that i dont habe time to study math and need to study for bio instead. Thank you.

[@PrimeNewtons]

Good luck on Bio.

[@Woobbled]

@PrimeNewtons I have no chance but thanks 🙏

[@leif1075]

​@@PrimeNewtonsyou cam also jjst put B plus V or just B wkthour x after the B in the partial.fraction decomp..jjst wondering why yu didnt do thst way

[@eng954]

i had solved this integration some years ago for keeping my knowledges alive. the result just the same.. this teachers tells with very clear and understandable english. very symphatic too.

[@marv9013]

This Channel is new to me and is so cool. It gives me chills:)

[@dragoscalin4883]

Bine de tot. Un profesor priceput, cunoscător al matematicii și pasionat la infinit, în același timp și un pedagog extraordinar. Artificiile de calcul sunt foarte importante la calcularea integralelor nedifinite(primitive de funcții) și nu numai la acestea, în matematică în general.

[@adw1z]

In fact, it is also possible to deduce the anti-derivative of such a generalised integral: ∫dx/(x^n + 1) for n positive integer using partial fractions and some complex identities to get a real answer. ∫ dx/(x^n + 1) = -1/n [ Σ{k = 1 to n-1 odd} f(x,k) ] + 𝟙{n odd} 1/n ln|x+1| + C, where: f(x,k) = cos(πk/n) ln(x^2 - 2cos(πk/n)x +1) - 2sin(πk/n) arctan[ xcosec(πk/n) - cot(πk/n) ] Plugging n = 3 into the above will give the exactly same answer as your video, like magic! Michael Penn derived this very result in a video for anybody interested, but it had a few mistakes. Could be an interesting video idea here

[@peternyekete6802]

Good observation

[@leif1075]

If irs ln why isnt it jjst ln 1+×^3 since that epuld nebthe derivative and jjst add a 3×^2 term usijg integration by parts...I don't see how your explanation is clear sorry..thanks for sharing .

[@FYP_010]

Can you reference the said video link here?

[@adw1z]

@@FYP_010 I can’t send links it seems, the video is called “generalising a calc 2 integral” - Michael Penn

[@mallikarjunaraokotikalapud4828]

Thanks sir. You are reminding the subject to me at my age of 65yrs.

[@arthurkassis]

I learned an "alternative" quicker method to do PFD integrals, but seeing the answer I got, it's not pretty at all, and it's: if you have a fraction like f(x)/g(x) and degree(f)

[@srisaishravan5512]

Thank you mr newton. For naking videos on integrals. Lets goo

[@juergenzhang9133]

Really like your style of teaching and presenting. God bless you!

[@arjunnn.9]

I'm not lying this was a 5 mark question in my School pre boards exams. I couldn't solve it, and this video got recommended. Thank you sir.

[@PrimeNewtons]

5 marks is too small for the effort involved. Sue the teacher 😂

[@spectre5815]

I'm from India watching your videos and learning at 2am night

[@Chillaxer599]

A beautifully clear explanation of a very instructive integral. You’re a natural teacher. 👍

[@tomchen8636]

Thank you for your video-it takes me back to my college years long ago. Even today, I was able to solve this problem in just 17 minutes. At 70 years old, I’m still working in IT and running marathons!

[@SriKrishnaSaravanan]

❤❤❤❤ Thank you very much sir for teaching us. Don't stop teaching sir ❤❤❤❤

[@SmilingDiamondRing-jt5ps]

This man is really my inspiration

[@vishalmahi]

Love the way you explain the solution❤

[@Kosekans]

I remember doing this one in a college course some 25 years ago. Nice one! 👍 Btw: Excellent teaching there.

[@Sharingan-y]

It is simple 8 number question in my 12th exam and i can solve it easily in 4-5 minute maximum but i like the way you are teaching and i appreciate it . ❤

[@rubenchavez2630]

In the partial fractions You can use the heaviside method + generalization of the formula for undetermined coefficients for a positive irreductible polynomials

[@denisb_MG]

17:40 this is true if the derivative of u is 1, for example u connot be sqrt x, or x*sqrt x, if it was true the problem was already solved.

[@HakiMaths]

Nice one. We can use the heavyside method to find A, B and C very quickly.

[@raymondseligman7003]

I think I have watched every one of your videos not even beginning to understand them as you began but following your explanations I caught on. You are a remarkable teacher. Again I would ask where do you get your background from and do you teach math at some location. Thanks and stay safe

[@taposgupta9641]

You explained it very nice as I'm a Mathematics Graduation student I just loved the way you explained it ❤

[@vash7468]

The sound of the chalk pressed against the board is therapeutic.

[@mikehughes6582]

I really like your low key teaching method.

[@2night_real]

Noo way, I did the same integral at my math lesson at uni today😂, as you said never stop learning🔥

[@bilongoralucas8068]

I really much addicted the way you tackle maths staffs❤

[@unkown9685]

The video that made me to subscribe your channel..😊 Thank you sir!! 🙏🏻 From India..

[@randomhooman3236]

currently in my final year of college been more than 4 years since i have studied integrals but just randomly ended up here took me back to those lockdown days when i was stuck solving indefinite integrals on summer afternoons for hours integrals are the best thing about maths

[@鋼然]

This classic problem looks simple but actually involves so many tricks😯.

[@Robin_9098]

If these type of questions come in mains I will dance in the examination centre for a second.😂 Well we can only expect in the CBSE board. I am not making fun of you but ❤ you are very nice at explaining 🎉🎉 very nice thanku.

[@cappmasters7253]

Sir you made a mistake , since you said you subtracting( A=-B)-(A=B+C) , you are supposed to change the sign of C

[@shaharmoskovich4794]

Hi. Great lecture We will be glad if you show that it can be also solved with complex analysis method.

[@rohangt1]

Hey Professor, I love that you are doing integrals. There is 1 indefinite integral which came in CBSE Class 12 Board Exam in the year 2014, India. As far as I remember, that integral is: Int(1/((cosx)^4 + (sinx)^4)) I was wondering if you would like to solve it.

[@DhirajGupta]

18:09 there must be (+) sign before 3/2 please check 😅

[@M.Farzan-B]

How beautiful God created the black man. Unmatched presentation. I like your Board, Cap and your Voice too!

[@laurenslavielle8957]

Hi ! Thanks for the video ! I have 2 more or less relevant comments to do. First one (and easy one) : the absolute value on x²-x+1 is useless as it is always positive Second one (trickier) : As the anti-derivative is not defined on x=-1, the constant C can be chosen differently on both side of the domain of the fonction. We can chose a C1 for (-infinity,-1) and C2≠C1 for (-1,infinity). So there are in fact a lot more anti-derivatives of 1/(1+x³) than described in the final answer :)

[@ghaithNahdi-rn4xb]

u have good smile when u teach ❤

[@NYlivinginTN]

Great video! I have the same hat!! Lookin' good, P. Newtons.

[@maths01n]

Keep up my fellow Mathematician content creator ❤❤❤ well solved

[@juanortegon9898]

Sir, that was an amazing explanation.

[@jaimemargarit2202]

👏👏👏Beautiful solution

[@boguslawszostak1784]

After all, the decomposition into partial fractions is a standard method for integrating rational functions.

[@mohandchaoui7924]

Thank you! Un calcul captivant..

[@Supercatzs]

another great video as always.

[@preoalex8298]

Such a nice way of solving the integral

[@karelvanderwalt3625]

3:47 make that an identity i.e true for all x. then esp. for x = -1 (Heaviside cover-up) ; and x = 0 and x = 1

[@renatoalcavi4052]

Podemos reescribir: 1/(x^3+1)=1/2×[(x^2-x+1)-x^2+(x+1)]/(x^3+1) Luego, separamos la integral de los 3 sumandos del numerador en 3 integrales. Notaremos que son integrales directas: I1=int 1/2 * 1/(x+1) -> Ln I2=int -1/2 * x^2/(x^3+1) -> Ln I3=int 1/2 * 1/[(x-0.5)^2+(√3/2)^2)] -> arctan Saludos.

[@doge_69]

I love your enthusiasm

[@bjornfeuerbacher5514]

Nice. :) You could have done it a bit more general, for 1/(a³+x³) instead of only for 1/(1+x³). It's not much more complicated.

[@peternyekete6802]

Thanks for a very good video.

[@JulioMirena]

Muy interesante e importante éste Integral, pero las letras y los números son muy pequeños en el desarrollo de la solución. Los problemas se deben explicar con letras y claros, para poderlos entender, gracias y disculpe. Amen.

[@SounakSaha-sx8zc]

Isnt it easier to multiply and divide by 3 and use the formula int f'(x)/f(x)=log|f(x)|+c

[@Maths786]

Sir please do a limit question which was came in JEE Advanced 2014 shift-1 question number 57 it's a question of a limit lim as x-->1 [{-ax + Sin(x-1) + a}/{x + Sin(x-1) - 1}]^[{1-x}/{1-√x}] = 1/4 You have to find the greatest value of a It has 2 possible answers 0 and 2 But I want the reason that why should I reject 2 and accept 0 Because final answer is 0 Please help 😢

[@jackramirez9900]

I’m new to integration since I’m just taking calc bc and on power rule still so why not just rewrite it to 1+x^-3 and then integrate which I think is x-1/2x^-2 + C

[@jaxoncr]

because 1+x^{-1/3} is not equal to 1/(1+x^3) = (1+x^3)^{-1}.

[@kishansuthar2765]

what if we multiply n divide with x and use IBP?

[@christoskettenis880]

Very good tips!

[@m4thsolution]

7:20 ada yang salah sepertinya itu pak... A+B=0, A+B+C=0, jadi, C=0, A+C=1, maka A=1 dan B=-1

[@TonicTrail]

I like his attitude.

[@sckani3432]

Nice, sir. S Chitrai Kani

[@R097-p2y]

i feel hydrated

[@Ahmed-kg2gf]

Method goes like this y=1/(x³+1) =(x²-x+1)/(x³+1) - (x²-x)/(x³+1) =1/(x+1) -(x²-x-2 +2)/(x³+1) =1/(x+1)-(x²-x-2)/(x³+1) -2/(x³+1) Recall 1/(x³+1) =y Thus y=1/(x+1) -(x²-x-2)/(x³+1) -2y , recal that x²-x-2=(x+1)(x-2) y=1/(x+1) -(x-2)/(x²-x+1) -2y y=1/3 (1/(x+1) +(2-x)/(x²-x+1)) Integrate this ,it is very easy

[@Andy-ju8bb]

Never seen partial fractions done that way. I was taught the cover-up method that BlackPenRedPen uses. Good to learn another way to do it.

[@bjornfeuerbacher5514]

The cover-up method only works when you only have (different) linear factors in the denominator.

[@Andy-ju8bb]

@@bjornfeuerbacher5514 Thank you for the info.

[@etiennejj3262]

Woah! Nice!! . *now do the integer of 1/1+x²*

[@danielsnyder3563]

Ultimate Question....... How do you get your Blackboards so clean?

[@ThenSaidHeUntoThem]

I treat the board before every video 😅

[@just-saying]

AFTER MY YEARS, MY CALCULUS IS GETTING RUSTY. THANKS FOR SHOWING THIS

[@skc4188]

Why is it mandatory to rationalize a fraction with a rooted denominator? I never understood that, and feels like artificially extending the resolution of the exercise

[@PrimeNewtons]

Not madatory

[@skc4188]

@@PrimeNewtons Oh, OK. I just noticed that many videos on YT about math say about "having" to rationalize fractions with roots in denominators, even though the resulting number or expression is otherwise the one the exercise asked for.

[@ciapennap900elarusenindel_9]

@@skc4188 This demand comes from old school school teachers. Consider the case back in the old days where you didn't have a calculator, access to any computer, not even a logarithm table. Typical school problems involve small integer numbers. Now, after you have manually computed a square root (that's what you were taught at school) of a 1-digit number to, say, 5 digits, what is easier: manually deviding a 1-digit number by your 5-digit result or doing it the other way round? Once such a demand has been formulated in text books it will stay there for awhile ;-).

[@rashid-ik]

Amazing ❤🎉❤

[@purplerose4647]

Incredible thanks a lot broo

[@shaxyyy69]

Ngl this concept is asked for 5 marks in my exams and guess what? I get recommended this video 😂

[@ikmg887]

hey is there any possible way of contacting you bcz I found out about thr coolest relationship ever but I don't understand why it exists for a^x = x to be true a must be between 1 and e^1/e and e^1/e is surprisingly the maximum value for x^1/x can u explain how this happened please I can't sleep because of it

[@ikmg887]

I really really really would appreciate a video about it 😭🙏

[@ikmg887]

at a = e ^1/e the derivative of both sides would be equal since x would be the tangent of a^x at a = e^1/e

[@ikmg887]

which is why it's thr final value since any point bigger than e^1/e would result in no answers (u can check in desmos when u change a to be less or more than e^1/e)

[@ikmg887]

now how do I relate this to d/dx(x^1/x) = 0

[@ikmg887]

this is all over the place I'm sorry my thoughts are scattered

[@HappyMunkhondya]

Sir please we need simpsons,trapezoidal,mid point & their error bound 🙏 please sir//your helping us a lot🙏

[@Lucky-ks7ob]

Interesting ❤🎉

[@VenuprasathM-f3f]

Thank you a lot mannn❤❤

[@Mmm---mmm]

I got one last week in class and it stumped me: prove that for any integer n, 3ⁿ+7ⁿ-2 is divisible by 4

[@PrimeNewtons]

I like this. Let me take a look.

[@bjornfeuerbacher5514]

Can't you simply look at this mod 4? Both 3 and 7 are equal to -1 mod 4. So this becomes (-1)^n + (-1)^n - 2. For even n, this is obviously equal to zero, and hence the original expression is divisible by 4. For odd n, this is equal to -4, which is equal to 0 mod 4, and hence again the original expression is divisible by 4.

[@Mmm---mmm]

@@bjornfeuerbacher5514 That's clever

[@Mukit-hy5vq]

Damn!!Great work

[@bricedoyle4780]

I wish this was my Calc 2 Professor/ TA

[@nevgongivuup]

more integration problems please ❤

[@maths01n]

Added my subscription

[@ayushChoubey-zs2mf]

Exactly what I did 😅😅

[@anuragprohg4366]

You can solve it very easily by Integration 1/1+x^3 Integration 1/1+x^2.1/x Answer=Tan^-1(x).log(x)+c

[@sweetpumpkin4586]

Thanks brother

[@ruihongqiu1120]

very detail thank

[@ankush_alonso]

Hey try integral (tanx)^3dx very interesting

[@Misha-g3b]

0,5tg²x+ln|cosx|+const.

[@ankush_alonso]

@Misha-g3b how did u proceed with cause I solved this around 1 year back with my friend

[@ankush_alonso]

@Misha-g3b if started with tanx=t^3 than u will get the answer but it will be lengthy

[@chitradevi9919]

5:51 so cute right

[@hamzaHamza-km2ng]

(x+1)(x^2+2x+1) = (x+1)^3

[@PrimeNewtons]

Incorrect factoring

[@lornacy]

Love it

[@Misha-g3b]

(1/6)ln[(x+1)²:(x²-x+1)]+0,(3)V3arctg[(2x-1):V3]+const.

[@ericgold3840]

Beautiful

[@dinoortolani6794]

nice channel subbed

[@Алекс-в8ш]

Intergrate fractional part because it makes no sense.

[@naveenmurali611]

Jee aspirant like it

[@Rajan-s4j]

👍👍👍

[@Ticavg15]

❤❤

[@Matematyk2024]

SUPER