Integration - Free Formula Sheet: bit.ly/3XCT6oz Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: ua-cam.com/video/4Nj3BErKiBU/v-deo.html
I got a 98% as my final calculus-1 grade. I had a great professor but I was also taking physics and we had to already know a lot of the calculus concepts, even calc 3 concepts, from the beginning and this guy helped me so much!!
To hopefully save others from the confusion I went through: there is a mistake in the first 2 minutes of the video where -5 should be 1 over -5. This is subsequently corrected at 2:17.
Your channel has made concepts which seemed so difficult in my lecture actually appear to be simple. I watch your videos on Calculus and Chemistry and gets A's in these classes thanks to your help!
Thankyou soo much for enlightening our minds! You have the best way in tutorials. It helps so much how you solve them step by step, rather than just talking and showing slides like other tutorials. Keep it up! May you continue to help other students like me! 💖
These exponentials have been KILLING me in my calc II/III (accelerated) course. It really helps seeing examples and not just staring at a basic formula. Thank you, kind sir.
You helped me indeed sir i always pass out when it comes to this mathematical problem but now i can breath now and too excited to watch your helpful video.be blessed sir always
Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on Integrating Exponential Function by Substitution in Calculus Two. The Exponential Function is one of the easiest functions to integrate in all of Calculus assuming that it can be integrated in closed form. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
That would be fine if -1/5 * dx was the same as -1/5 * du, because that's what [-1/5 integral of e^u dx] gives. Regardless, it should have been -1/5 integral of e^u du because "dx" stands for differentiation in regard to x, which there isn't any. It needs to have du there.
Love your videos! You get right to the point. How does one do a definite integral of a function of t with respect to t if you have an x as an upper limit and a constant as lower limit. Example: INT -8 to x of e^(cos(t) dt If you have a video on this the link would be great. Thanks!
This may be a bit late of a response, but maybe it will be helpful to others passing through the comments. The problem that you are describing sounds like it would require the fundamental theorem of calculus. I believe he does have a video on this that could be checked out. Also, depending on when someone is reading this comment, I might have a video on that topic on my channel as well that could be helpful too. I'll come back and link it here when I do.
In my add math book it is quite a similar method as what you are teaching basically Calculus . I m learning this so I can take on pre calculus / calculus its fun but sometimes I feel bored cramming this in my head .
Im confused at 4:33 , isnt the derivative or e^x is e^x1-1 which x becomes 0 or cancelled out. It means it only remains with e? So the derivative of e^x = e
Whaaat?? Still searching youtube for math help?? Are the videos from 2006 REALLY helping?? um, yes. math hasn't had some dramatic change in the past 15ish years. this video is from 2017 anyways.
My Calc 1 class seems to have harder subjects than other Calc 1 classes at my uni, do you guys think this course material is considered Calc 1 or is it in the Calc 2 range? Luckily I am doing well in the class so i hope Calc 2 will be e breeze next semester
The material in this specific video is most likely considered calc 1, although not all calc 1 courses at universities have the time to cover these sections for exponential functions. So sometimes you may see it in calc 2 courses.
So generally, if there are several exponential terms in a (ir-)rational function, f(x)= (e^ax + e^bx)/cx), then u=ax because, a>b, so.... -->du=ax*dx. But if all the terms are have the same coefficient value of, a=b in the ^ax/^bx term, but they may or may not have different signs, of their exponent, then, f(x)=(e^ax + e^--ax)/x, and the entire numerator (or denominator) will be used as the term for u-substitution. This to cancel out their (ir)rational counter part in the integrand. Am I getting that right?
No, x is the exponent of e. What part exactly are you confused with? How he subtracts the exponents to reduce the function? Let me know, I would be glad to help you understand! Also, I have a video on my channel on integrating exponential functions that can be found in my calculus playlist if you'd like to check that out. It may be able to help you as well! I'll link it here for your convenience: ua-cam.com/video/tHPPdn7PTHQ/v-deo.html
@@petarpejic1468 Ah, I see what you are referring to now. I did not fully understand your original question. So yes, e^x is the same as exp(x), but the x in e^x can still be treated like other exponents. The multiplication rule of adding exponents still applies (For example, e^x * e^x is e^(2x) because x+x=2x ) and the division rule also still applies as shown in this video from the organic chemistry tutor. For a student that is learning calculus for the first time, treating the x in e^x like any other exponent is really all that is needed to be understood, but 3B1B's video is certainly a great resource if you want to dive further into what is actually going on.
This multi-colored writing and drawing software is nice. What is the name of this software you are using? I would like to use it for teaching classes. Thanks in advance.
Mate how do u solve word problems. I have word problem that says "mina weighs 80. And plans to start a diet. The rate of her weight is given by the derivative dw/dt= -3e^-0.004^t. Where w is weight and t is number of weeks. After how many weeks will her weight be 70 kg?
To check your answer you would need to take the derivative of your answer and compare it to what was in your integral. This will be different for every integral, but generally you want to determine what derivative rules to use based on the features of your answer. It is a composite function? -> use the chain rule. Is it a quotient of two functions? -> use the quotient rule. Is it a product of two functions? -> use the product rule. And so on. Does this help? Let me know! And if you are interested, feel free to stop by my channel, I have a playlist of all my own calculus videos that may be able to help you! Have a great day!
When you use the power rule for integration, you divide by the exponent after adding 1 to it. So 1/2 + 1 = 3/2. Then you divide by 3/2 which is the same as multiplying by the reciprocal of that fraction, which is 2/3. Hope this helps! I explain how to integrate basic functions like this in one of my own videos, so I will link it here for you, it may be able to help you understand better! Link: ua-cam.com/video/5T-3P-q2L38/v-deo.html
To deal with the integral in the form of INT f(g(x)) g'(x) dx We always use the substitution u = g(x) du = g'(x) dx so the term g'(x) in the original integrand can be absorbed
Integration - Free Formula Sheet: bit.ly/3XCT6oz
Final Exams and Video Playlists: www.video-tutor.net/
Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections
Next Video: ua-cam.com/video/4Nj3BErKiBU/v-deo.html
Bro, got a 92% on calculus for engineering test 2 because of your videos ! ty
I have got 97% ☺
Al- Bayan I must have Alzheimer’s, cause I don’t remember asking
couldnt imagine getting less than 100%
@@bobsacamento7879 dude he's just saying lmao chill
AR KI sorry
I got a 98% as my final calculus-1 grade. I had a great professor but I was also taking physics and we had to already know a lot of the calculus concepts, even calc 3 concepts, from the beginning and this guy helped me so much!!
To hopefully save others from the confusion I went through: there is a mistake in the first 2 minutes of the video where -5 should be 1 over -5. This is subsequently corrected at 2:17.
appreciate the heads up thank you!
Thank you. How considerate of you. I paused the video racking my brain and notes trying to figure out why.
Thank you! I went to the comments for this reason
Ya, I remember doing that on assignment and getting that question wrong. Now looking at it again I see where the mistake was.
Thanks m8, I came looking at the comments to see if someone had noticed this as well.
I always watch the ads because this guy deserves the ad revenue
Yes😍
Your channel has made concepts which seemed so difficult in my lecture actually appear to be simple. I watch your videos on Calculus and Chemistry and gets A's in these classes thanks to your help!
You are a life saver. I have exam tomorrow and I am watching this right now.
Single-handedly saving my mathematics career
this video saved me ., just on time with my lecture class at school. So I can catch up with
Thankyou soo much for enlightening our minds! You have the best way in tutorials. It helps so much how you solve them step by step, rather than just talking and showing slides like other tutorials. Keep it up! May you continue to help other students like me! 💖
Really your explanation is best and you are the best teacher in the UA-cam, keep going fowrad
Nanci pi ,u have really helped me a j.s.s.3 student especially on integration also u Patrick thanks a lot.
thank you for this . im glad , I skipped my maths lecture bcs of im have some important things to do . this help me ! pls , make more !
thanks a lot. Your explanation is brief yet thorough.
These exponentials have been KILLING me in my calc II/III (accelerated) course. It really helps seeing examples and not just staring at a basic formula. Thank you, kind sir.
You helped me indeed sir i always pass out when it comes to this mathematical problem but now i can breath now and too excited to watch your helpful video.be blessed sir always
Ur explanation is magical, I thought this was so tough but now I get it!
I really wanted to cry
😭😭😭
Can you make a video for double integration for exponential functions whose power has also a power?
You are the goat 🐐 you've saved countless students from failing
you just helped me last week and now im here again
You are saving my 2020 semester.You are the best
Lol. I applied integration by parts and got stucked.
You saved my time.
I love how you don't skip steps
Professor Organic Chemistry Tutor, thank you for an awesome video/lecture on Integrating Exponential Function by Substitution in Calculus Two. The Exponential Function is one of the easiest functions to integrate in all of Calculus assuming that it can be integrated in closed form. This is an error free video/lecture on UA-cam TV with the Organic Chemistry Tutor.
totally agree
♥️ty...this means so much 2 someone like me who doesn't understand anything in these topics♥️
Thank you so much, I really appreciate your help making my life so much easier
He saved 1100 burning souls and we have 51 casualties.
71 now
116 now
124 now lol
About 3,800 peeps saved now let’s gooo
This was so helpful. QM 1 is an A. Could you make a video on Exact Differential Eqns?
thank you , you goddamn king . you just saved my life
At 2:05 its "du" not "dx", he said it but forgot to write it ✔️
Mistake at 2:05. It shouldn't be [-5 integral of e^u dx] but instead it should be [-1/5 integral of e^u dx]
That would be fine if -1/5 * dx was the same as -1/5 * du, because that's what [-1/5 integral of e^u dx] gives. Regardless, it should have been -1/5 integral of e^u du because "dx" stands for differentiation in regard to x, which there isn't any. It needs to have du there.
He corrects it at 2:30!
Thanks a lot .now after watching your video my concept has clear now. thank you sir🙏
Love your videos! You get right to the point.
How does one do a definite integral of a function of t with respect to t if you have an x as an upper limit and a constant as lower limit. Example:
INT -8 to x of e^(cos(t) dt
If you have a video on this the link would be great. Thanks!
This may be a bit late of a response, but maybe it will be helpful to others passing through the comments. The problem that you are describing sounds like it would require the fundamental theorem of calculus. I believe he does have a video on this that could be checked out. Also, depending on when someone is reading this comment, I might have a video on that topic on my channel as well that could be helpful too. I'll come back and link it here when I do.
Thank you for making this video. It really helped me in solving integration qs
really attractive teaching method
YOU'RE A LIFE SAVER😭😭
Thankyou sir while deriving an equation your vedio help me.
I was able to understand it clearly.. nice 💪
bro yr the best man! hope for the best for u in ur future!
This guy has saved so many calc grades LOL
This is beautiful. How math works
In my add math book it is quite a similar method as what you are teaching basically Calculus . I m learning this so I can take on pre calculus / calculus its fun but sometimes I feel bored cramming this in my head .
Thank u so much, very clear examples
It's a great explanation . thank you
So simple but really useful
Im confused at 4:33 , isnt the derivative or e^x is e^x1-1 which x becomes 0 or cancelled out. It means it only remains with e? So the derivative of e^x = e
this is a really a good tutorial.I LIKE IT
I don't understand why did we add (-1) in 6:15
Can anyone help me ... Thanks
The derivative of e^(-x) is e^(-x)*(-1) because the derivative of -x is -1*x^0 once you apply the chain rule
Try making U = e^(1/x^2) and see the magic! 07:53
This helped me in the last second of doing my activity lmao thank u so much
mate you're a hero
For the last example...would it be the same if the fraction is flipped (e^x on top)?
Whaaat?? Still searching youtube for math help?? Are the videos from 2006 REALLY helping??
um, yes. math hasn't had some dramatic change in the past 15ish years. this video is from 2017 anyways.
did u just argue ur self in a comment.
nice
@@skyglitcher4355 Haha, was referring to an annoying ad often played on math-related videos. Always poppin up on every video i watch
Thank you for your great work 🙏🙏
Oooh bhaiiiii ur like an angel to meeee
you are much better than my professor lollll
You are a life saver, thanks so much ♥️
nice jobs ,this is really awesome and helping to drive a stop mind.
Great explanation
this channel gives me something to do when ever im not sipping lean. just kicked t he mud 2 weeks ago and have been here everyday #6DaysSober
My Calc 1 class seems to have harder subjects than other Calc 1 classes at my uni, do you guys think this course material is considered Calc 1 or is it in the Calc 2 range? Luckily I am doing well in the class so i hope Calc 2 will be e breeze next semester
The material in this specific video is most likely considered calc 1, although not all calc 1 courses at universities have the time to cover these sections for exponential functions. So sometimes you may see it in calc 2 courses.
Best video easily understandable
Your the man, thank you!
you're a God
Thank you so much
You deserve a Grammy award..... always saving my ass
So generally, if there are several exponential terms in a (ir-)rational function, f(x)= (e^ax + e^bx)/cx), then u=ax because, a>b,
so.... -->du=ax*dx.
But if all the terms are have the same coefficient value of, a=b in the ^ax/^bx term, but they may or may not have different signs, of their exponent, then,
f(x)=(e^ax + e^--ax)/x, and the entire numerator (or denominator) will be used as the term for u-substitution. This to cancel out their (ir)rational counter part in the integrand.
Am I getting that right?
I just subscribed to your patron. soooooo good
10:10 I don't understand isn't e^x = exp(x) so x is not an exponent but rather an input to a function?
No, x is the exponent of e. What part exactly are you confused with? How he subtracts the exponents to reduce the function? Let me know, I would be glad to help you understand! Also, I have a video on my channel on integrating exponential functions that can be found in my calculus playlist if you'd like to check that out. It may be able to help you as well! I'll link it here for your convenience: ua-cam.com/video/tHPPdn7PTHQ/v-deo.html
@@JKMath ua-cam.com/video/ZxYOEwM6Wbk/v-deo.html starts at 7;16
@@petarpejic1468 Ah, I see what you are referring to now. I did not fully understand your original question. So yes, e^x is the same as exp(x), but the x in e^x can still be treated like other exponents. The multiplication rule of adding exponents still applies (For example, e^x * e^x is e^(2x) because x+x=2x ) and the division rule also still applies as shown in this video from the organic chemistry tutor. For a student that is learning calculus for the first time, treating the x in e^x like any other exponent is really all that is needed to be understood, but 3B1B's video is certainly a great resource if you want to dive further into what is actually going on.
7:08 was legendary
5:50 isn’t this integral of coth(x) which is ln(sinhx)? But sinhx is 1/2(e^x - e^(-x)) whereas this video’s answer looks like ln(2 * sinhx).
thank you :) this video really help me a lot dude :)
bro u r a legend
Your so brilliant brother
in 5:19 where does the multiplying by 2/3 come from, it appears out of nowhere
This multi-colored writing and drawing software is nice. What is the name of this software you are using? I would like to use it for teaching classes. Thanks in advance.
The software is called SmoothDraw. It's free. :)
2:54 why did u substituted u by x^4?? If we follow LIATE rule it will be x^3
How do you know what to substitute for u
thank you so much! you legit explain everything
I appreciate this!
Mate how do u solve word problems. I have word problem that says "mina weighs 80. And plans to start a diet. The rate of her weight is given by the derivative dw/dt= -3e^-0.004^t. Where w is weight and t is number of weeks. After how many weeks will her weight be 70 kg?
Thank you I'm in 12th grade an things get tuff
How about the checking? Our prof, require us to get the checking using the differentiation. Any suggestions to get easily the checking🥺🤗
To check your answer you would need to take the derivative of your answer and compare it to what was in your integral. This will be different for every integral, but generally you want to determine what derivative rules to use based on the features of your answer. It is a composite function? -> use the chain rule. Is it a quotient of two functions? -> use the quotient rule. Is it a product of two functions? -> use the product rule. And so on. Does this help? Let me know! And if you are interested, feel free to stop by my channel, I have a playlist of all my own calculus videos that may be able to help you! Have a great day!
i still dont know why he got 3/2 as the exponent a 5:10
He applied integral rules, hence, 1/2+1=3/2 and the denominator is 3/2 as well
I get cgpa 3.8 because of you
I have calculus exam tomorrow someone should wish me luck🙏🙏
would ln(e^x-e^-x) + c not simplify to x+x +c or 2x+c as ln and e are inverse functions?
Ur the best there is
I got stuck with a radical exponent how do i solve it?? 😭
Thanks man....u helped me...
Thank you 👍🏼😊
I dont understand how you derived -e^-x and got e^-x(-1) at 6:24
(-1) times (-e^-x)=(e^-x) because the negative coefficients basically cancel out
It is good for person that is confused
5:14 why did we multiply with 2/3 ???
u^(3/2)/(3/2)
When you use the power rule for integration, you divide by the exponent after adding 1 to it. So 1/2 + 1 = 3/2. Then you divide by 3/2 which is the same as multiplying by the reciprocal of that fraction, which is 2/3. Hope this helps! I explain how to integrate basic functions like this in one of my own videos, so I will link it here for you, it may be able to help you understand better! Link: ua-cam.com/video/5T-3P-q2L38/v-deo.html
Your realy helped me pro thank you
this is too easy... im here trying to find the integral of e^(e^x)
Johnyy_ take the natural log twice lol
Just take e^x as u and integrate it
It will be a nonelementary integral = Ei(e^x) + C
I have intégral of Racine of 2×(ro/b)×e ^-(t/b) ×t.
ro ,b are constantes
6:42 how does it work why was -e^-x multiplied by -1
YEA WHY
Diravitive of -x is -1
seriously..... {e^x-e^-x(-1)} ...... it's all wrong
Isnt it the chain rule
@@githice it is not wrong
At 7:48 why in this example , if we set U=e^(1/x^2) we obtain a different answer ! if someone knows why plz reply
To deal with the integral in the form of INT f(g(x)) g'(x) dx
We always use the substitution u = g(x)
du = g'(x) dx
so the term g'(x) in the original integrand can be absorbed
How can one know with clarity the function that should be U???
Excelente profe