integral of sqrt of tanx

Рет қаралды 29,965

Prime Newtons

10 ай бұрын

In this video, I showed how to integrate the square root of tanx

Пікірлер: 82

@Moj94 10 ай бұрын

This is one of those integrals that looks "simple enough" when you're taking an exam.

@jayniesgottagun 10 ай бұрын

My God, you're smart and have a gift for teaching. I plan to absorb all you have to give.

@paulstjean8598 27 күн бұрын

I do enjoy your patience and step by step breakdown. Too bad I'm retired and no longer have students to share this with. Keep it going.

@Jop_pop 10 ай бұрын

I've never dived this deep into integrals before and this is probably the most complicated integral ive seen explained so succinctly

@syed3344 6 ай бұрын

I did it like this: I=int(sqrt(tanx)) Now cosider a new integral J J=int(sqrt(cotx)) I+J=Int.(sqrt(cotx) + sqrt(tanx)) I+J=sqrt(2)*Int.( (sinx+cosx)/sqrt(sin2x)) we know that sin2x = 1-(sinx-cosx)² I+J=sqrt(2)*Int.( (sinx+cosx)/sqrt((1-(sinx-cosx)²) Now substitute sinx+cosx=t (cosx+sinx)dx=dt I+J=sqrt(2)*int.( dt/(sqrt(1-t²)) I+J=sqrt(2)*sin-¹(sinx+cosx)+c1 NOW I-J=Int.(sqrt(cotx) - sqrt(tanx)) I-J=sqrt(2)*Int.( (sinx-cosx)/sqrt(sin2x)) we know that sin2x = (sinx+cosx)²-1 I-J=sqrt(2)*Int.( (sinx-cosx)/sqrt(((sinx+cosx)²-1) Now sinx+cosx=t (cosx-sinx)dx=dt (sinx-cosx)dx=-dt I-J=sqrt(2)*int(-dt/sqrt(t²-1)) J-I=sqrt(2)*int(dt/sqrt(t²-1)) J-I=sqrt(2)*ln|x+sqrt(x²-1)|+ c2 J+I=sqrt(2)*sin-¹(sinx+cosx)+c1 Subtract them -2I= sqrt(2)*[lnx+sqrt(x²-1)-sin-¹(sinx+cosx))+c3

@josephparrish7625 10 ай бұрын

I love this problem. And, of course, I’ve seen it before. How would a student who has never seen it know what the first move would be? I used to tell my students, “now that you’ve seen me do it, remember the first move!” My students would ask, “how did you know how to do it?” and I would answer, “I saw my professor do it in college!” Lol Anyways, I love your very clear and detailed explanation of a great problem. As always, you amaze with your teaching skills!

@savitrinamdeo-zr5jo 9 ай бұрын

Very nice way of explanation nice n clear voice

@bravo2992 9 ай бұрын

I think our plan was to get rid of root

@Phantom_Reaper_ 8 ай бұрын

@@bravo2992getting to 2t²/(t⁴+1) is natural enough, but the steps after that just seem too complicated for any student to do in the first time imo

@user-ci9ko7rf7f 7 ай бұрын

That's great !!!

@sivasakthisaravanan4850 5 ай бұрын

There are people who can do it when they see it for the first time, without being taught! But these days as we have Wolfram Alpha, we don't have to manually do any integration😊

@jesusandrade1378 6 ай бұрын

That form of the final solution is the most simplified and symmetric form, because you can also express the inverse hyperbolic tangent as a logarithm, and yet another form if you use partial fractions after 2t^2/(t^4+1)

@rhm5158 7 ай бұрын

I used to do this stuff over40 years ago and it’s amazing to me how much I don’t remember. You just blew my mind.

@trivikram4962 4 күн бұрын

i can finally binge ur videos, as i have just started integration. thanks

@murdock5537 7 ай бұрын

This is amazing. Many thanks for this awesome "journey".

@PrimeNewtons 7 ай бұрын

Glad you enjoyed it!

@cesarmiranda2205 7 ай бұрын

Outstanding explanation, you are the guy, I really enjoyed, best regards from Brazil.

@paulinofm 5 ай бұрын

Maravillosa integral y maravillosa solución. Thanks from Spain. !!!!!

@user-xd8yu4wc5z 2 ай бұрын

Keep going your videos are the highlight of my day❤

@Viewpoint314 5 ай бұрын

Nice clear writing for this interesting integral.

@NamregSelaur-up4or 6 ай бұрын

I solved that integral with two maths skills. 1. Using substitucion. 2. Completing the perfect trinomial.

@saarike 4 ай бұрын

Huh, what an integral. Thanks for sharing. Never stop learning or you not living 👍👌👍I have to watch this many times...

@arungosavi5698 7 ай бұрын

Mind boggling ,sir

@oscarfranciscosantanafranc8948 6 ай бұрын

You are very smart. God bless you!

@rob876 8 ай бұрын

You made a difficult integral look easy.

@user-ti9xi1nt1i 10 ай бұрын

Sir you are a genius at mathematics thank you

@servictorovich2576 8 ай бұрын

однозначно, красивое решение. Достойно похвалы

@maxborn7400 9 ай бұрын

I remember once in school, one of us wanted to troll the teacher, so we asked, "what is the integral of e^(tan(x))". While it was a joke, I have sometimes wondered about it. Integral of e^(sin(x)) is a Bessel function of order 0. Integral of e^(tan(x)) shows some interesting, convergent properties. But I never get around to formalising it, only numerically studying it. Would be interesting if we could some day find an analytical expression for that, or just a "special functions" recursive series (I think I have that somewhere).

@user-ug3vn2mj7t 8 ай бұрын

Good math go head for more thank you man 👍👍👍

@joelmacinnes2391 4 ай бұрын

I knew that the integral of 1/x^2+a = 1/sqrt(a) .arctan(x/sqrt(a)) + c but not why that was the case, thanks for the video!

@Necrozene 3 ай бұрын

I love your stuff man! Love maths. Maths is my "God Zero"!

@wasagamer001 10 ай бұрын

Thanks for the video sir !

@stinkybohoon71 4 ай бұрын

Excellent Teacher, congrats

@TopRankX 10 ай бұрын

Keep going man! Love what you do ❤

@jesusandrade1378 6 ай бұрын

Some integrals require more than 2 or 3 consecutive substitutions or methods to get a solution, and there may be equivalent solutions.

@madsniper5927 8 ай бұрын

And that was perfect Thank you for the lesson

@michalkorczyk4189 4 ай бұрын

if this video is too long or slow for you, press F12 and type "document.querySelector(".video-stream").playbackRate = 3;" to konsol

@amolgameryt7159 9 ай бұрын

I had solved this question recently it kinda esy If you are preparing for competitive examinations

@kawenjanathan6538 3 ай бұрын

Thank you for the save ❤

@user-kg7xw5ip2l 3 ай бұрын

You are my favorite ❤❤❤❤ bro

@jesusmartinez9662 10 ай бұрын

your videos are the best!

@herbertsusmann986 3 ай бұрын

This is why they came out with books of tables of integrals! People doing real work want to look it up in a book and not try to derive it from first principles and probably get a sign wrong or something!

@lukaskamin755 7 ай бұрын

Wow, that was intense, kinda a detective story to find the suspect (the integral) LOL

@ethanbartiromo2888 4 ай бұрын

I actually watch all of your videos in 2x speed lol

@moorecable 5 ай бұрын

Learned a lot. But why not let u be cos(X) . Then it's sqrt-(lncos(x)) . You can get ride of the negative as cos(-x) is also cos(x).

@PrimeNewtons 5 ай бұрын

If I knew it was a better option, I would have used it.

@user-mj6rr1xn3t 10 ай бұрын

Thanks, integral sqrt sen x

@martys9972 8 ай бұрын

Great derivation, but when tanh instantly turns into tan for v/sqrt(2), at 23:48, you really should have mentioned that correction or edited over it.

@PrimeNewtons 8 ай бұрын

I'll have to watch it again to see what you're referring to. Thanks for the feedback.

@bibliophilesayan320 10 ай бұрын

Sir can't we use The method of by parts to solve this problem??

@devonwilson5776 6 ай бұрын

Greetings. Thanks for sharing.

@lebesguegilmar1 8 ай бұрын

The maestro. Very inteligent your tecnic of solution. The same strategy of solution if the int \sqrt{\cot x}dx? And too \int \sqrt{\sec x}dx? The variable \phy and \theta not same? Here in the Brazil congratulation teacher

@haithamsuneer2182 7 ай бұрын

Hey sir i hope ur doing well can i ask a doubt after we get the integral as ∫2dt/(t²+1/t²) cant we factor the deno as {(a²+b²) = (a+b)² -(2ab)} SO WE GET 2∫dt/(t+ 1/t)² - √ 2² then just apply the formula so the final answer in terms of t will be 1/√2 {ln [(t+ 1/t)+ √2] / [(t+ 1/t) - √2]} + c

@tamilchelvanramasamy8733 6 ай бұрын

Great Sir

@piyushhh.54 10 ай бұрын

Actually this is a very famous question in our board(exam conducts) education system

@abhishekpathak4973 10 ай бұрын

That was wonderful ❤

@AvrajitGRoy 10 ай бұрын

Amazing man!

@vadimtokman123 6 ай бұрын

Could you differentiate to prove there is no errors? BTW, great job!!!!

@PrimeNewtons 6 ай бұрын

I did

@noid3571 10 ай бұрын

I had this setup on my exam and I was stuck, I just couldn't figure out what to do and wasted so much time. So after the exam I put this problem into symbolab, since nobody got the answer, and I couldn't beleve the result Thanks for the video : )

@emmanuelseiman2725 10 ай бұрын

Cool but sqrt(tanx) +1/sqrt(tanx) is always >1 (ex: 1.46 for π/6) so you have to use coth−1 instead of tanh−1. It is always necessary to pay attention to the domain of definition of hyperbolic trigo. functions tanh−1 ∈ (-1;1) and coth−1 ∈ (-∞;-1)∪(1;∞)

@jesusandrade1378 6 ай бұрын

You are right

@vashu471 10 ай бұрын

I solved this question yesterday in my school in one try ✌️

@Occ881 6 ай бұрын

Do you study in college or highschool...you might be genius

@Harbingersknight21 10 ай бұрын

Thanks this problem was in my text book

@Vikram-xc3pb 6 ай бұрын

Just another ordinary problem for Jee advance aspirants😂😂

@roddos 6 ай бұрын

Piękny wywód.

@lindsaywaterman2010 6 ай бұрын

Brilliant!

@nibirhasan4142 10 ай бұрын

how can we write root 2 φ as the result of that integration? as tanh^2 x+ sech^2x=1

@paulmatthewduffy 10 ай бұрын

WOW!

@Shashi_227 10 ай бұрын

Your 📸 are most recommended

@omaraladib2165 8 ай бұрын

حلوة ولكن الطريقة طويلة

@gideonkudgorgi226 7 ай бұрын

O Bruv, why is the answer more complicated than the question itself 😅😅😅😅

@jesusandrade1378 6 ай бұрын

Because the integral is more complicated than the derivative (the integrand). That is why integration is more difficult than differentiation. Differentiation is just mechanical/algebraic manipulation and simplification, and integration is an art. And many elementary expressions, functions, or integrands don't have elementary integrals/antiderivatives