It's awesome that you resolve a large span of integral problems in a straight forward manner. Usually when I'm stuck in a problem I lose too many hours of study reviewing basic concepts or trying to understand why wolfram alpha solved such problem this or that way. Because you cover many specific cases I can now watch a short video that helps me with that particular thing I'm stuck at and move on to other exercises. Your videos are helping a lot with my productivity! Thank you!!!

@darcash1738

4 ай бұрын

Yes, wolfram does these problems strangely. I love these ones a lot because they work out quite beautifully like taylor series. You follow it down subtracting from the power by 2 until you either get ln|secx| or x. Because it keeps on becoming integral(tan^(n-2)), if the original n is even it is x, if odd it is ln|secx|. Lemme just use 't' to represent tan to make it simply and omit that it is a func of x in some examples of integrals. I'll omit the +c too: - t^2 --> t - x - t^3 --> t^2/2 - ln|secx| - t^10 --> t^9/9 - t^7/7 + t^5/5 - t^3/3 + t - x - t^11 --> t^10/10 - t^8/8 + t^6/6 - t^4/4 + t^2/2 - ln|secx| Memorizing the quick way for all of these (tan, sec, sin, cos, x^m * (lnx)^n, e^ax * x^m) is much better than using the reduction formula. ofc it's a good exercise to do the integration by parts to derive them too. Maybe I wont even use these, but the mere act of figuring out how to maximize speed and how to best remember things increases your intelligence. Idk how many ones i want to remember but theyre pretty fun

This man is a Godsend. Thank you Mr. Pens

Isn't the integral of tan(x)=-ln|cos(x)|+C?

@alinalee2658

3 жыл бұрын

͔ equivalent to what he wrote

I wonder 1/2sec²x + In|sec xl + c also can be answer

@jetray2805

2 жыл бұрын

Same bro

There is already a negative sign in front of integral tan x dx so negative and negative will be positive right?

Can I take u= sec(x) and du= sec(x)tan(x)dx ?

cant we use di setup for 1:30?

Excuse me! If integral of (tanx)^n dx ?please help me!

Watching foriegn teachers like u gives. Me a diffrent taste in maths...

@Unknown_User940

3 жыл бұрын

#indian

sir why cannont we solve by taking log and the power down ?

i love your videos lol they are so fun

Thanks for the video , but I have to mention that the channel's name is very creative, I liked it

Fantastic video, Great job!!

Best channel i found

thankyou sir ... your's new student from INDIA

Why did you take 1/2 in the last step

This video helped a lot, thank you very much. Would really appreciate you would post/share the video where you take integral of tan in terms of sine and cosine. @blackpenredpen

I added tan(x) and subtracted tan(x). -tan(x) became another integral. Then, I factored out tan(x) and I was left with tan(x)(1+tan^2(x))dx U=tan x Du= (1+tan²(x))d,

@prakharsharma2517

2 жыл бұрын

Thnx it was too easy

Thank you. Great explination

I like the way you teach and amazing

Suscribed. THANK YOU! Is that ball some kind of 'on the fly' translating device prototype? -Or just your mic?

@blackpenredpen

9 жыл бұрын

CofeeAuLait LOL, finally I got a comment about the Ball!!! It's my mic!!

@maxpowergaming3496

8 жыл бұрын

+blackpenredpen i don't believe such huge mic exist, it seems nuclear device to me lol

@blackpenredpen

8 жыл бұрын

+Ali Kill LOL!! It is a mic, a magical mic!

@CarlLeo0015

6 жыл бұрын

Dude i subed u bcuz of that mic lol it looks cool

What is the answer ,,, when limits of same integral are 0 to π/2

Awesome, thank you

I think in our programme we do not have the rule you used

Thank you Mr. Pens

I am confused man. In the back of my book, the answer is different. Way different....?

We can also use the reduction formula to help us however it can be verbose. it is also worth mentioning that this is also equivalent for restricted x values to 1/2(sec^2(x))-ln(|sec(x)|)

Thanks sir for your big help

what happens to the "du" or sec^2dx

@veritasiumaequitasius3530

3 жыл бұрын

When you integrate u du, this is integrating just u with respect to u. the du (derivative of u) disappears. Likewise, since sec^2(x) is the derivative of tanx, it will disappear. Differentiate it to reverse this, and you'll see that you get du or sec^2x back

Can we instead let u = secx instead of tan ?

@naitratyagi240

Жыл бұрын

Yeah I did it that way but it's not giving the same answer

youre awesome!

Thank you!!!

Perfect 👌

Nice teachings carry on

why is it when you do the sin(x)/cos(x) method you get (1/2)sec^2(x) for the first part of your answer. I am referring to the answer your student got in the other video.

@yassinekh4382

3 жыл бұрын

They're both right

Thank you so much!

Excellent bro

Tan^3x=sin^3x/cos^3x -ln(cos^3x)+c is it right?

Thanks for solution

Int. Of tanx dx =Ln |Cosx| too in this example. Am I Right ?

@shalinikumari6130

3 жыл бұрын

Yes

@HusseinAli-kk9tn

3 жыл бұрын

@@shalinikumari6130 ok thanks 🤍

Thank you!

I'm understood😍

Sorry to ask, where did 1/2 came from? I'm still learning:

@ddzhong4476

2 ай бұрын

搞懂 ∫xdx是怎麼算的 你就能理解了

Thank you so much

not got postive sign meh.whynegative sign

Thx!

thank you

Thanks a lot we follow #Love4Study

ln|cosx|+tan'2x/2+c

@HusseinAli-kk9tn

5 жыл бұрын

Both are true..

@armandoolmos1816

4 жыл бұрын

And I thought I was being crazy as hell for getting that answer smh , now I know it’s the same . :)

I liked the part when he used the black and red pens

thanku sir..

You could put topics in Arabic, French or translation in one of the previous two languages

@lucasm4299

7 жыл бұрын

Hydaru Lique French, Yes

may i ask a question plz : why do you intergal tan x | secx| is there's a defined law for that or what becouse in our education we intergal tan to ln cosx directly and thanks😊

Perfect

Woo...👍👍☺️

Gracias

Thnk u sir .

gracias chino

Integral tgx= - ln(cosx)

@aleph4464

2 жыл бұрын

You can write cosx as (sec)^-1 and get -1 in front of the ln, so -ln(cosx)=ln(secx)

Wow thanks

Integral of TANx = -ln(COSx), not -ln(SECx) ...... right?

@blackpenredpen

7 жыл бұрын

The Observant ServantTM they are acuallly the same. kzread.info/dash/bejne/dXyY082igdO-ntY.html

@Jc123

6 жыл бұрын

-ln(cosx) = ln(secx) -ln(secx) = + ln(cosx) So they are not the same thing

@guisilva9815

6 жыл бұрын

ln(sec(x)) = ln(1/cos(x)) = ln([cos(x)]^-1)= -ln(cos(x)) so they are the same

@guisilva9815

6 жыл бұрын

Jc123 You are think like those functions are equivalent to -x and x , they aren't.

@takeone_do

5 жыл бұрын

ohhh I see what you're tryin to say, but because integral of tan x = -ln(cosx) = ln(secx) and the integral is already minus so it is minus ln(secx).

Thanks

lan bunları lisede öğrenen tek millet biz miyiz ya

@tibet9478

5 жыл бұрын

sanırım ama lisede basit görüyoruz

Bu caponların kafa çalışıyor abi bunlar hep otobüste kitap okumaktan biz hala kafayı cama yaslayıp hayatla ilgili önemli kararlar alalım

Nice

The second part is wrong, the anti of tan(x) should be loge|cos(x)| instead of sec(x)

@quantumlove7950

4 жыл бұрын

no. his answer is right. -log(sec x)=-(log(1/cos x))=-(log1 - log(cos x)) = log(cos x)

@alissabrave424

2 жыл бұрын

@@quantumlove7950 Thank you so much for the explanation!

Hey i think you maybe rong :/ just and the end,because tan=(sen/cos) then you can do there u'/u=ln (u) so the answer it woukd be ln (cos)

@blackpenredpen

9 жыл бұрын

Hi Claudia, this is just an approach. I also worked out sin cos approach here, check it out! kzread.info/dash/bejne/dIlkm6mOYd3JpJs.html

@CofeeAuLait

9 жыл бұрын

Claudia Solis Your way is also valid. There are many ways to integrate this.

@blackpenredpen

9 жыл бұрын

Claudia Solis I just realized what you meant, integral of tan(x) is either -ln|cosx| or, equivalently, ln|secx| , both with +C of course kzread.info/dash/bejne/dXyY082igdO-ntY.html

@Nisbo360

7 жыл бұрын

-ln (cosx) or ln (secx) are both correct.

ln |cosx| + 1/(2 cos^2x) + c, and i dont even need to know what sec is ;)

Can't your mike be a little small? It's really funny.

just use reduction formula of tan...u can get rid of this tedious process

数学の先生より分かりやすいw

Nobita is teaching now

I watch this video 2024 ❤

From india

كنت محتاجه اتأكد من حلي بحثت بالكوكل وطلع لي طالبه سادس من العراق خلي نشوف هم يجي واحد عربي هنا 🧐🤔

Ncert maths class 12

이걸 끝까지 봤어야했는데 시발. 오늘 2차고사에 나왔음 시이이발

...

GET A MIC

خرا عليك حيدر وليد وصلتني للاجانب باسئلتك

you are WRONG. the final answer is 1/2tan^2x+ln|cosx|+c. Remove your video and redo a new one with the correct answer. Thanks!

@mil9102

6 жыл бұрын

Chance Kassi Well, I know it's been 4 months but anyway -In(sec(x)) = In(cos(x))

The second part is wrong, the anti of tan(x) should be loge|cos(x)| instead of sec(x)

@ME-tj4wm

4 жыл бұрын

nop, just watch his video about tan(x) and you will undertand.

@kyleakin_2123

Жыл бұрын

its right

@mitadrusen1668

Жыл бұрын

Yeah integral of tan x is - ln cosx

@user-tx3oy4hk8m

6 ай бұрын

​@@mitadrusen1668 And what is ln(cosx)^-1 Genuis? Isn't it lnsecx?

@rayquazabtc9131

2 ай бұрын

​@@mitadrusen1668 That's why education is important 😂🙏🏻 ln|secx| or -ln|cosx| both are same things😂😂🤣🤣🤣🤣🤣🤣🤣🤣 average onlyfan country