integral of sqrt(tan(x))/sin(2x)

[@snbeast9545]

I have a heart attack whenever I see "integral" and "root of tan x" in the same sentence.

[@darthsion3844]

The two make a VERY deadly combination 😢😢😢😢😢😢

[@CheapPhysics]

I have made this maaan!!!!

[@PunmasterSTP]

I think we all do 😥

[@jackkalver4644]

Whenever you see sqrt(tan x), it often pays to use u=sqrt(tan x) to convert the problem to something manageable.

[@yusuke85]

1) double-angle formula 2) u=tan(x), x=arctan(u),dx= du/(1+u^2) 3) sin(x)= u/(sqrt(1+u^2)) and cos(x)= 1/(sqrt(1+u^2)) 4) inside of the integral is du/(2 sqrt(u)) 5) the result is sqrt(u)= sqrt(tan(x)) +C

[@carlosabrill4851]

Nice substitution bud, I struggled a little with this problem, Even tried to use weierstrass substitution

[@karangujar317]

Hey!Found the easiest method!Just divide numerator and denominator by (cosx)^2 and you are done :)

[@blackpenredpen]

Ah ha!!! I see it now too!!! Thanks!

[@LOL-rg8wb]

OH YEAH!!!!!!!!!!!!

[@Aramil4]

Karan Gujar you mean right from the onset? Can anyone explain? :/

[@PawanKumar-kv4it]

Aramil4 writing sin2x as 2sinx.cosx we have √tanx /2sinx.cosx dx multiplying by cos^2x and simplyfing 1/2×integral sec^2/√tanx dx now just substitute tan=u

[@glydon-w2w522]

Noob that's all the way same ...

[@thanjavurvlogs1307]

Super explanation I caught but I used to leave c in sec x during exams😢😅😂

[@StephenMarkTurner]

I did the same sub as Fabien (u = sqrt(tanx)), but only subbed for du, left everything else in the x world. It quickly simplified to integral of 1 du.

[@RedIceberg]

You could also just do a u sub with u=tanx, then convert cos^2x/sinxcosx to 1/u.

[@eleazaralmazan4089]

Keep making these integral videos! Your the best!

[@Ravikumar-wy2dj]

You’re*

[@themathworm4984]

You can also do it by just applying the second formula of sin(2x)= 2tanx / 1+ tan²x ....and so on

[@fabiengiudicelli1455]

Thanks for all your vids. I just found an other way to integrate sqrt(tan(x))/sin(2x), you just have to do the u-substitution at the beginning with u=sqrt(tan(x)). I think it works, almost at the end you have u^2.cotan(x)du ; but u^2 is nothing but tan(x), give to integrate 1 in the u-world which equal to u + C , and u is sqrt(tan(x)), finally you have sqrt(tan(x)) + C.

[@blackpenredpen]

That's brilliant! Thanks for the method!

[@fabiengiudicelli1455]

I am glad to read a compliment from blackpenredpen's teacher! I learn a lot from your vids so thanks to you, I am so grateful!

[@faezwahid7354]

fabien Giudicelli can you show me how you do by substitution u=sqrt tan x ??

[@blackpenredpen]

In fact, I just did that on the other day kzbin.info/www/bejne/p4asYominrqGoq8 Thanks to Fabien

[@fabiengiudicelli1455]

Thank you Wahid for your interest, Blackpenredpen was faster than I to answer your question :) , a chance because his vids are very well illustrated, it is better than I could do. I wish a nice end of year to both of you.

[@prollysine]

Gratulálok a feladathoz, a megoldás meglepő és mulatságos ! Szuper !

[@prakhargupta3739]

write sin(2x) as 2tan(x)/1+tan(x) and you can directly go to the last step

[@Concordeagle]

That microphone though..

[@timmurski2075]

I love that your continuation arrows look like integral symbols. thank you for your awesome videos.

[@blackpenredpen]

hahahah! thanks!!!

[@zerospeed6412]

If you had written sin(2x) in terms of tangent it would be as simple as sharpening a pencil.

[@karandabas128]

Absolutely

[@darkseid856]

It would have been Way easier if you expressed sin(2x) in terms of tanx Sin(2x) = (2tanx)/(1+ (tanx)^2). 1+ (tanx)^2 becomes (secx)^2 and goes on top . After simplifying we get integration of [(secx)^2 dx] ÷(2√tanx) And It can be easily solved by taking u=tanx. Solved in 3-4 steps .

[@duduomer5149]

It can be solved in one substitution: t =sqrt(tan(x)) dt=dx/(((sqrt(sinx)*(cosx)^(1.5))*2) integral(dt)=t+c=sqrt(tan(x)) 

[@Akshushah_1205]

You can also just apply Sin(2x)=2tan x / 1+ tan^2x and then 1+ tan^2x as sec^2 x and then we can just take tan x = u

[@xyrokai6343]

Say tanx = u² and sec²x.dx = 2u.du Do the substitutions it gives you 2u²/(2sinxcosx/cos²x) and then that makes 2u²/(2tanx) Tanx was u² So the original integral becomes simply 1 but in u-world. Take the integral and it gives you u + C substitute back and it gives you √tanx + C

[@lohram4443]

Hi, you could use parametric formulas for sine and cosine.... indeed you have t=tan (x/2), in this case when parametrizing sin (2x) you just have t=tan (x) and then can write dx=dt/(1+t^2).. check that.. makes it soo easy.

[@hique6]

A

[@aeroflySL_2021]

Hi bprp! Stating straight with u = tan x is easier right cuz sin2x also can be written ofinterms of tanx then a lot cancels of?

[@taranmellacheruvu2504]

You can start by doing the double angle formula for sin and dividing the numerator and denominator by cosx twice to get: int (sqrt(tanx)sec^2(x)/(2tan(x)))dx Then u=tanx gives you int(sqrt(u)/(2u))du which is sqrt(u)+c or sqrt(tanx)+c.

[@tomatrix7525]

These videos are unreal keep it up

[@nonedone]

dude, that was thug life

[@vitorsousa5390]

That's interesting to note that this integral is an improper integral. With the integral function only making sense at a value different than zero, because the derivated function is not defined at x = 0

[@МирославНачев-в4щ]

F(-sinx,-cosx)=F(sinx,cosx) => we can use the substitution t=tgx; sinx=t/(1+t^2); cosx=1/(1+t^2); dx=dt/(1+t^2)

[@BRUNOLOPESDF]

Please, solve integral of sqrt(tan(x)).

[@blackpenredpen]

BRUNO LOPES I did it recently!!

[@gnsoares_]

kzbin.info/www/bejne/bKeTgqSAbZyamq8

[@bojanglesfries]

guy's its simple. Just multiply it by sin(2x)

[@Dharmarajan-ct5ld]

Why write such long solution ? Write sin 2x =2tan x / (1+tan^2 x). Cancel √tan x : note it is non zero. It is over in one step. Kindly consider

[@rotemlv]

The way I'd to it is by bringing it all to the numerator, after the double angle. sq(tanx) * cscx * secx, then multiply and divide by secx, split the two between the last two terms and you get (after u sub): sq(u) * (1 / u) * du Yeah yeah everything over 2.

[@fourier07able]

On the board, after (1/2)*Int [sec^2 x/sqrt(tan x)]dx, all of the remain he wrote is unnecessary because of Int [sec^2 x/(2*sqrt(tan x))]dx = sqrt(tan x) directly since d/dx(sqrt(tan x)) = sec^2 x/(2*sqrt(tan x), the integrand!

[@PunmasterSTP]

That was some very nice manipulation 👍

[@wallybaldemor8523]

Just cancel the denominator. Voila

[@ayushfirodiya6083]

Put tanx = t^2 and just put values of sinx, cosx and sec^2x in terms of t . The whole equation gets cancelled out and you are left with integration of just dt. Found this easier method to solve this

[@Lily-zd6dx]

i love his accent !

[@keshavmurali98]

Ah, I had a variation of this in my school textbook (sinx cosx in the denominator instead of 2 sinx cosx) and my brother told me the cleanest way was to substitute u^2=tan x I tried canceling like this, but I then got stuck after a few steps for some reason. Good to know it can be done like this as well.

[@psykp930]

Your are a motivation, man! ❤

[@chidhambaramgl5135]

Nice bro...good work I like it bro...

[@carlosabrill4851]

That's the problem I'm stucked on, it is from the Stewart's book

[@Kanal263]

Isn't there an integral which you can't solve? I'm Always very impressed, when i See you solving the Most complicated integrals

[@hemanthsirvi]

I was able to solve all of this in my mind without even using pen and paper

[@pipertripp]

I just multiplied top and bottom by sqrt (tanx) right out of the gate. it gets you to the u sub setup in fewer steps. I like the clever algebra with sqrt(cosx) though.

[@blackpenredpen]

Ah i see! thanks for sharing

[@jessewon4226]

Thanks for the lecture(integral obsession | integral of sqrt(tan(x))/sin(2x)). Do you mind if I ask you a question? Is there a shorter way to approach upon the SAT or real exam in Math class? Please let me know.

[@shaunakkulkarni4679]

Do what he does rly fast

[@dagmawidemelash3209]

You Have Helped A Lot. Thank You!

[@miterun]

Actually sqrt(cos^2) = |cos|. Why this factor is ignored? Why do you take cosx? It is only one part of solution

[@Tsskyx]

Hey wait a second, I thought the dx at the end of the integral had no meaning, and now you took it at 6:20 and did some math mumbo jumbo with it. I didn't know you could do that.

[@GAMERCREEDbrickjet]

it does have meaning, you are multiplying all the integral stuff by dx

[@Tsskyx]

Why?

[@GAMERCREEDbrickjet]

watch 3blue1brown's essence of calculus. it has a great way of explaining this stuff

[@Tsskyx]

I did watch that already. I don't think it answered my questions.

[@GAMERCREEDbrickjet]

integral is basically a formula for finding area under a curve. Area is height times width. For the finest approximate, split the curve into infinitesimally wide rectangles under the curve. The height of these rectangles would the value of y at every given point, so f(x). your width is going to be an infinitessimally small change in x, or dx. so your area is going to be the sum of all the rectangles with height of f(x) multiplied by dx. you can write this like sigma notation where A=S f(x)*dx and thats how why dx is used

[@wallybaldemor8523]

@3:38 its like a conjugate, my opinion only

[@ultravidz]

That was insane I was not able to solve it

[@michaelboy6605]

You can turn sin2x into 2sincos, pull out the 1/2 from the integrand, then make a u substitution for u=sqrt(tanx). Then set up a right triangle with angle of x and opposite of u^2 and adjacent of 1. Since du=sec^2/2u dx, you can make sec^2 = u^2 + 1. Then sub in “[2u/(u^2+1)]*du = dx” into integrand, and you get awesome cancelation that ends up being integral of 1 du which is u which is sqrt(tanx)+c, your way is really cool I like it

[@tarekhisham4573]

Assume tan equals u from the beginning and the process will become much simpler and easier

[@selcukpolat2371]

I am enlightened.... Thank you so much!

[@khalidmustafa7102]

multiply cosx and devide cosx then it will become simple

[@carllacoste5824]

How sin(2x) turns into 2sin(X)cos(X)?

[@HeyKevinYT]

search it up its a basic identity that can be easily derived from sin(a+b) formula

[@germanorozco4072]

Muchas gracias me ha sido de gran ayuda

[@luismariabiaggioni8514]

Menos mal que te entiendo por lo que escribes, porque si fuera por lo que dices en tu inglés achinado, estaría frito. A veces me parece que haces un misterio de problemas que pueden resolverse en forma más sencilla. Igual, gracias por tu esfuerzo y amor por las matemáticas.

[@Suyog_07_12]

What a lovely solution!!

[@adnanace5867]

why not just simply, put tanx=t^2 and multiply by sec^2(x)/sec^2(x), we would get answer in literally 2 steps .

[@abeltesfahun6192]

good job, man

[@elbisho2045]

awesome!!! keep making videos

[@avisinghvi6170]

Man you are great!

[@jhosefroberth6816]

Muchas gracias realmente me ayudó un montón

[@muhammedg-tips1584]

i solved this in 3 minutes ♥

[@dineshpethad5856]

dx/dy+2ytanx=sinx How to do this D.E

[@yassinezaoui4555]

I think writing sin(2x) as 2t/(1+t²) would be better and make it more easier 🤔

[@rishabhmahajan6607]

Just make tan(x) = t2, and multiply numerator and denominator by sec(x), and it is solved in one line

[@Jeff-wc5ho]

What's so special about that tan sub? It seems to be a very powerful tool to solve otherwise nasty integrals.

[@Aek1961]

Διαιρώ αριθμιτη και παονομαστή με cos^2 x. Έχω ολα tanx και στο αριθμιτή έχω sec^2 x!!!! Και τελειώνει το παραμύθι .......

[@koustavhalder8839]

hey you could have directly substituted sin2x=2tanx/1+tan²x...i guess it would have been easier..

[@nishchhal-zb4xc]

It took me 30 seconds man!

[@viletomedoze5036]

Can someone please turn 5.sin x(.cosx)^3 to (√tanx)

[@plislegalineu3005]

now suppose you don't know this integral solve a diff-eq dy/dx = y/sin(2x)

[@dingwahliaw5361]

👍👍👍👍👍

[@FunctionalIntegral]

You are making it too complicated. Just substitute u=sqrt(tan(x)) and the rest is trivial.

[@ahmedarfat]

Nice

[@divyajyotibose5769]

Can you make a video on integration of {(4e^x+6e^-x)/(9e^x-4e^-x)}dx

[@TheRealSamSpedding]

That was nifty

[@ericknutson3296]

Integrate(sin^x(x))dx=????

[@muffymypup1871]

good job. amazing. thnkyou

[@GUYANESEGT]

what kind of witchcraft is this

[@HeyKevinYT]

mathematicus

[@dudewaldo4]

Use IBP with dv = sqrt tanx because you have already done the video on that :P

[@angadsharma4715]

The answer is wrong dear it will be -2/√tan x +C

[@itsallfun4964]

Bro explained he is smart and dumb at the same time....u can express double of sin in terms of tangent....and then use substitution method....bro just takes 6 steps....

[@chessandmathguy]

Very nice!

[@jntnayem1394]

I'm sorry, but I don't know your name, sir.. May I allow, please???

[@benedictaamoako-gyamfi6733]

cool...you are brilliant and handsome

[@Jeff-wc5ho]

beautiful problem :)

[@williamtachyon2630]

Cool!

[@atmsc4nd4l]

Wow. Same method. Coincidence? 😅

[@azoznail1223]

I solved it with an easier way

[@wilsonoliveira7447]

Cool...

[@Gamma_Digamma]

You could have just written sin2x in terms of tan as 2tanx/(1+tan^2x), could have probably taken less steps...

[@manishkumar-qz9gx]

Ans the( √sin2x.dx) Tell me ans

[@justforfun2238]

Trivial

[@ujueije5762]

Stop using Mathematica Alpha & Wolfram Alpha online software.

[@jeshurunluke5573]

These are really simple integrals... he's a calc teacher he shouldnt have a problem with something like this

[@eswerreddyduggireddy5275]

Hi

[@SatyanarayanaMudunuri]

Unimpressive. It is simple to write sin 2x = 2tanx/sec^2 x, and let t = tanx

[@marcushendriksen8415]

That was a long way of saying that the denominator basically worked out to be 1, just saying ;)

[@agwuokoman7976]

Thanks alot

[@dhanushsk1549]

The most easiest way write sin2x as 2tanx÷1+tan^2x

[@manishrai6857]

Substitute sin2x by 2tanx /1+tan^2x and substitute tanx as t 😎🤓💯🧠🤙