I remember doing loads of these integrals in my engineering degree. Very long and challenging to do but in the end very rewarding. Love how the t=tan(x/2) brings all of the trig functions together. Very beautiful.

There has to be a movie where the victim says "we're in the t world now".

I'd never heard of Weierstrass substitution, that's awesome!

@blackpenredpen

7 жыл бұрын

Yay! Btw, here's the intro vid kzread.info/dash/bejne/o52e2puzqJaufrQ.html

You and Dr. Peyam are one of the best math teacher in KZread!!! : )

1:32 whem u think its over, but it wasn´t even starting

This was so good. I'm an undergrad senior (fair warning, who has largely focused on discrete and abstract math since being free of calculus.) But this was something I'd never seen before. This vid is awesome (with the video on the substitutions themselves too).

I did this by multiplying top and bottom by 2-cosx and replace cos^2 x by 1-sin^2 x and split into 2 integerals One on them has cosx in the top easy to do and the other we can multiply top and bottom by sec^2 x to get sec^x in the bottom and function in term of tan x in the bottom

∫ 1/(u^2+a^2) du = (1/a)arctan(u/a) + c

@triton62674

5 жыл бұрын

THIS

In the integral of 2 / 3 + T^2 DT. Why not put the 2 outside and you'll be left with DT/ 3 + T^2 , find values of U and DU, and the final answer will be Ln | u | + C?

Fantastic video, you saved my life, greetings from Spain.

@blackpenredpen

7 жыл бұрын

you're welcome!

I enjoy this question, thank you very much

At 1:55, why can't you just instantaneously integrate that to 2/√3 arctan(t/√3), by using a^2 = 3 and the 1/(a^2+u^2) du formula?

@dealwiththebob3877

6 жыл бұрын

Kyle Rachman he did say you could in the video ... He continued onwards so that we saw the entire process.

@znhait

5 жыл бұрын

That is not a "basic" integral. How do you think it got derived in the first place? By using u-sub. This is also a problem that could easily be given in calc I exam meaning that the integral can't be taken for granted as it might in a class where the professor assumes that the students are comfortable with the well-known techniques of integration.

instead of u-sub, why didn't you do tan sub? or just write ot as arctan(t).?

Thank you very much - that was very helpful for me :D Greetings from Poland

Does it work for 1+cosx denom?

I think this could've been done a bit simpler. After Weierstrass substitution, instead of factoring out a 3 from the denominator, you could've just used substitution where t=sqrt(3), and then factor out a 3.

@ioanungureanu1429

8 ай бұрын

you're totally right

I think this method is not taught with the standard of the sum. Replacing 2 and cosx by submultiple angles.

can you do 1/sinx+2

Hi solvs this ones Integration of [(sinx)^2/(a-bcosx)]dx lim 0 to 2π where a & b are constant ok please

Some + signs are pretty equal yo some t letters...

There are thousands of integrals. Maybe start a higher math playlist like linear algebra ?

@blackpenredpen

8 жыл бұрын

Hi Nick, Unfortunately I am not teaching linear algebra. I may do a playlist in differential equations sometimes soon tho (but once again, it involves tons of integrals : )

@lakshaymd

7 жыл бұрын

YESS!!! Do differential equations please! I love your way of explaining and Khan academy like videos get too boring to bear after a while xD Differential equations would be really helpful

Can you evaluate this integra. (1/((cos 2X ) + a) as ( a ) is constant

@ernestschoenmakers8181

3 жыл бұрын

Well for this integral where a is any constant but where a>1 or a

Love you sir nice explanation

I din't know this sub but I had already done with euler sub after sub cosx by u. My result is (2/√3)tan^-1[(2/√3)(((sinx+1)/cosx)+1/2))], by diffentiation it works also!

What's all that t

Well done

Lifesaver

Thanks saved me pal

1/(3+cos(x)) t=Tan(x/3)??????

@santhanam2855

5 жыл бұрын

No. The t substitution is made to use the half angle formulas, thus getting sinx and cosx in terms of t. If 1/3+cosx then do the same thing the 2 or 3 doesnt matter for making this subn

please explain Integration of 1/a+cosx dx

@ernestschoenmakers8181

3 жыл бұрын

Please check out my comment above, there you see how it works.

Plese can u solve this eq. (1-cosx/2cosx)dx

@asadyamin4867

5 жыл бұрын

Simple, split into (1/2)(integral(1/cosx) - integral(1)) He made a video on integral of sec(x) already so, You get a final result of: (ln|tanx + secx| - x)/2 (+C)

@ndjdkskwkmcm4498

5 жыл бұрын

@@asadyamin4867 thank u So much😊

It was 2√3/3 but you said 2√3/√3

Smart way thank you bro

I don't understand why dx= 2dt/1+t^2 ?? Please tell me. 😦

@almightyhydra

6 жыл бұрын

t = tan (x/2) arctan t = x/2 2 arctan t = x 2 dt / (1+t^2) = dx as derivative of arctan t is 1/(1+t^2).

@dealwiththebob3877

6 жыл бұрын

B G watch his introduction video to the substitution for his explanation

I want to integrate the same equation from 0-2pi....if I am using maple,Matlab and symbolab, I will get 3.6275.....but when I use calculator, I will get zero (radian mode) and 2.0957 (degree mode), and if I use the final solution given in this video, I also get zero.

Thanku sir🤗🤗

That's an awesome way to integrate!! Thank you for the introduction. PS. Am I the only one, who at first glance read it as - 'weirdass'? XD

@AlgyCuber

6 жыл бұрын

xD

@ianmoseley9910

5 жыл бұрын

yes?

Thank you a lottttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttttt

"into the t world"

Good video with a minor mistake. You need to add the integration constant before substituting u -> t -> x. So, it should be 2/sqrt(3)*arctan(u) + C and the C should carry through to the next step.

Keep it up

Nice

Hiii broo. E model lo 1/1+ Tanx sum explain plss

@chitchaat68

Жыл бұрын

Reply plsss

Please start differential equations

@blackpenredpen

7 жыл бұрын

Abdur Rehman I did already

@111abdurrahman

7 жыл бұрын

blackpenredpen oops... I saw it later. You are doing a fantastic work. You have many more fans than you think. Please keep it up. Love from Pakistan

Why dt= 2/1+t^2 ????

@dealwiththebob3877

6 жыл бұрын

Play Ch do you mean why does dx = 2/(1+t^2) ?

@ernestschoenmakers8181

3 жыл бұрын

I think that you mean dx=2dt/(1+t^2) right? Well this can be derived from tan(x/2)=t, Now take the inverse tangent on both sides then you'll get: arctan(tan(x/2))=arctan(t) so: x/2=arctan(t) x=2*arctan(t), now take the derivative of x then you'll get: dx=2dt/(1+t^2), there's your answer.

Nice👍👍👍👍👍👍

ESSES VÍDEOS DEVERIAM SER TRADUZIDOS.TRANSLATION TO PORTUGUESE PLEASE

@thomasjefferson6225

Жыл бұрын

Learn English

Submultiple angles substitution is definitely easier than this method.

Excellent but I think you did a mistake. You didn't mention the constant.

@brightness8496

9 күн бұрын

😂 everyone do same mistake

If you take the substitution of t=tan(x), instead of tan(x/2). This doesn't give the same result. Why is that?

@amritlohia8240

6 жыл бұрын

tan(x/2) works because when you put it into the double-angle formula, which has a nice rational form, you get tan(x), which can be related to sin(x) and cos(x). Similarly, if the integral you want to evaluate is all in terms of sin(2x) and cos(2x), then t=tan(x) would theoretically work.

Great explanation. BTW , I am Indian.

@soumil5794

2 жыл бұрын

why did u feel the need to say you are Indian?

@iamrushi

2 жыл бұрын

@@soumil5794 Because Indians are everywhere.

@jmz_50

9 ай бұрын

​@@iamrushiI'm everywhere but I'm not Indian

What would you do if you had 4+5cosx instead of 2+1cosx.... Please help me I'll have to finish my home work...😅😅😅

@ernestschoenmakers8181

3 жыл бұрын

I guess you finished your homework now but the method stays the same.

use direct formula to save your time....

+C

help me:sinx=x/100

You can do integral of 1/2+senx ???

@blackpenredpen

7 жыл бұрын

Pascal Monet yea

@pascalmonet5729

7 жыл бұрын

I love you!