Integral of tan(x)
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- Опубликовано: 7 фев 2025
- We will discuss the integral of tan(x) by using u-substitution.
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Check out my 100 integrals for more calculus integral practice problems. ruclips.net/video/dgm4-3-Iv3s/видео.htmlsi=lTybJlpTMFdQINXr
Your positive attitude towards teaching us is the best part of this video. It pushes me to work harder, and also love math more! Thank you.
Stfu bitch
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Woah. I can’t lie this is probably the best explanation I’ve seen on RUclips. Props to you sir.
ABSOLUTELY WELL EXPLAINED
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You could have also multiplied by secx/secx to start, then you would have (secxtanx/secx)dx, then let u=secx. du=secxtanxdx, then the integral becomes (1/u)du. The answer would be ln[abs(u)] or ln[abs(secx)]+c.
Will Power WOW I LOVE IT! And now that's very similar to multiplying secx+tanx for integrating secx. Cool!
OR just dx/sec[tansqrt[2][co3)dx/dy1/E)
Over powered forbidden substitution bro.
This is the most wholesome math tutorial I have ever seen
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I've watched a ton of your videos. I was a math major/grad student/teacher, and you are the best math instructor I've ever seen. Congratulations on doing such a fantastic job!
Thanks for the explanation of the integral. I'm in calculus and I'm seeing integrals for the first time in my life, so much thanks.
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Perfect explanation. The less I have to memorize the better, this is really helfpul
Exactly my thoughts. I hate memorizing, and I'm really bad at it since I get anxiety on quizzes/tests and blank out and forget
You are a much better resource than all the textbooks in the world put together! Thank you so much... I loved the way you explained each step before you wrote something down.
Dividing du = - sin(x)dx both sides by -1 would do the trick too for those who prefer to solve it without mixing variables, but I like the way you explained it because it shows that solution has many paths and it's up to one to choose the one that suits best! Great video.
that "hi" just brightened my day
His shifting between pens is just outstanding!
THAT MAKES SO MUCH SENSE NOW!!! Thank you so very much for making it all click for me. Wonderful job teaching :)
Love how you explain step by step! Keep going my dude!
all my teachers are so bad I swear, thanks for explaining something clearly for once 😂😂
Soy salvadoreño, estoy aprendiendo inglés y estoy estudiando ingeniería, he entendido perfectamente a la explicación, muchas gracias y saludos! :D
You make me love more and more calculus!! Thanks for everything
Your English and solving skills are just great
Thank you so much for making integration a little easier to understand
This was the first RUclips video I watched today since the site went down!
Thank you for all the content . Keep spreading hope and positivity.
Thanks a lot for taking the time to explain how to take the minus away, it's not common. Much appreciated.
One of the best math channels on RUclips. Thanks a lot.
Thank you for your videos! You have helped me a lot. Your videos are straight forward, short and educational !
instead of converting tanx into sinx/cosx, we can take, int(1.tanx), then apply the UV/BiParts rule
Integration by parts doesnt work here
Never seen someone smile while doing calculus lmao, great video
The way u derivated tan x was good and ur way of talking was good 👍
Wow...30+ years since I learned this!
Nice review.
This is the greatest explanation
Don't understand what you speak
Due to weakness in English
But understand everything what you write
Love from India
Yes 🔥
dude i just discovered ur channel and i'm already in love with you !
You can multiply the tan(x) with sec(x)/sec)(x)
Then take the ln of the sec(x) because it's derivation sec(x)tan(x) and you're done
Yes! Nice one man!
True
You can use the fact that
itgrl(f'(x)/f(x)) =ln|f(x)|. So itgrl(sinx/cosx)=-ln|cosx| which just equals
ln|secx|.
The way you see ‘hi’ in the intro is so kiddy and cute. 0.1
f' time g'(f) is the derivative of g(f) where g and f are fonctions
Here f is cosinus (so f' is -sinus) and g is logarithm (so g' is the inverse fonction)
So tangent (sinus time the inverse of cosinus) is negative logarithm of cosinus
That’s how I would see it
you are thee best teacher ever,you have helped me alot God bless you and your family
In Japan, we learn this integral in high school ,18years old . Among world, high school students are not able to make out what he say,but I do it. This is not boasts but our prides .
dang we're in uni by the time we're 18 in malaysia and i only learned this in my second year (19 yrs). but i don't think it matters when we learn this? the only thing that matters is why tf am i learning this.. :')
This is mind blowing. For my test, I had to remember what the result was, but not the work behind it.
Thank you!!! You explained it so well, to a point where I can recite this during a test/exam if I need to. Just subscribed and look forward to the rest of your videos.
i was so stuck on that last step THANK YOU SO MUCH
Can we all just clap for him once now. He taught me more clearly than my old useless teacher 😂
you're good at what you do
I know i'm 5 years late, but I haven't seen anyone in the comments pointing out that the substitution isn't even necessary. sin(x)/cos(x) = (-1)(-sin(x)/cos(x)), so you can just throw -1 out of the integral and get a nice -sin(x)/cos(x), which is obviously the derivative of -ln|cos(x)|
You are a great teacher.
great video dude. Much appreciated
No problem!
@@blackpenredpen why isn't the answer just sec^2x + c? is there a difference between tanx and tan (x).
@@calvind7519 no, there is no difference.
Derivative of tanx is sec^2x.
Integral is the anti derivative.
We can also just simply the ln method, where u do it directly from the beginning
This blew my mind. Thank you
It could also be ln(sec x). Derivative of that is secx tan x over sec x. Secx cancels out.
I was wondering about this! Thanks!
It is obvious the result of the integral, because sin x = - (cos x)'. So it is true that if f(t) = integral of (g(x))' / g(x) dx, then f(t) =ln| g(x) | + c
best explanation video on youtube
Explained really well. Thank you kind sir.
Great explanation. It helped a lot!
Thanks for your clear explanation
The best substitution for this integral is u=cosx or u=secx
Substitution u=tanx still works but it is a little worse
If we dont want to convert into sin and cos we can multiply numerator and denominator by secx
and substitute u=secx
I love how he says hi in the beginning
Love from India
Thank you for the help!
Your content it's amazing!!!
I think that in integration , derivative of cos is sin so in exponent and logarithmic we can make it Ln|cos| + C
I don't understand where you are going but using sin x in the substitution method is wrong, because you will have "cosx (integral of u/cosx)"
Thank you, your videos are great!
Thank u sir. Your videos are very helpful
Nice explanation. Thank you.
EXCELLENT VIDEOS THANK YOU
Thanks for the great guide!
this is beautiful, thank you!
Thank You So Much Sir for uploading the solution!
Thank you so much, keep doing this great work dude.
U are amazing one and l want your comment as my best teacher below on how l can become a great one in mathematics like u🙏🙏
Note to anyone watching, this is integration by substitution, there are many ways of integrating.
Thank sir u have explained this question very efficiently
Thanks! I was confused because integral of tan is the odd one of all integral of trigo function
Nice way of teaching. Great 😊😊
amazing integral's man !!
excellent explanation.thanks lot
Thanks i have a huge home work & your vedio help me a lot
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Really straightforward and quick explanation thank you very much.
I can still hear my professor saying to my class that this integration is in every calculus book. It can even make a good quiz problem. Make sure to learn it well and simplify it.
Thank you very much sir
Thnx ,, very well explained.
is this method still working in 2024?
Patched
Couldn’t you use inspection such that, let y=ln|cosx| so dy/dx=-sinx/cosx. This means that the integral=-ln|cosx| which is the same as ln|cosx|^-1. This is also equal to ln|secx|. 🤷🏽♂️
Very well done concise video. Thank you.
Thanks I was having a doubt and u helped me solve it:)
Thank u very much sir 😇
Thank much more easy to understand
Thank you very very much
What I don't understand about your substitutions is why you substitute in terms of u AND x, or whatever variable(s) you happen to be using. The way I was taught, and which I believe makes more sense and it easier, is to simply substitute in what is equal. For example, at around 1:30 you have "du = -sinx dx". Why not just divide both sides by -1 such that you have "-du = sinx dx". From there you can sub in "-du" for "sinx dx", immediately plopping the negative sign on the outside. Is the way in which you perform this manipulation more formal? I find it to be far more confusing. Thank you so much for all of your work. You're truly inspirational! What kind've camera do you use brotha?
That works also when you substitute sin(x)dx to -du that will make it as -integral of du/u.
The amount of time I have rewatched this video because I can't remember this integral for the life of me.
Don't memorise the answer, just understand the process :)
@@quantum3075 Yess :)
Thank you Professor
Thanks sir I am Indian but your teaching style best
Thanks for the explanation
I love this guy so mush...
Thnks alot 😊 ... From Pakistan 🇵🇰
Short and sweet.
Can I solve it without 'u' term?
I mean directly.
Nah, u substitution is required
I want to share something wid you :-
tan x is nothing but sinx/cos x...we know that,if the differentiation of denominator appears in the numerator we always write log ( denominator).here,sinx is the differentiation of cos x...( but negative sign missing)..so,we can write,. -log( cosx).
the inverse of cos x is sec x...so, finally the integration of tan x is ln sec x..
Can we solve this by using integration by parts ?
I think it would be messy...u = sec(×), du = d(sec(x))/dx, dv = sin(x), v = -cos(x).... then you have evaluate the integral of vdu. Not easy.
@@JSSTyger thank you for explaining!
thanks for your generous help