wow! 0:48 how long did it take you to learn how to write in reverse? it looks like you're writing on a plate of glass with the camera on the far side of it. 😊 very cool effect. (and cool maths too but that "goes without saying")
Actually you can integrate inverse functions by integrating original functions and subtracting it from the area of rectangle formed by the integration limit, it works because inverse of functions are symmetric about x=y line.
@@deekshanaik2438 No,we can't integrate with respect to a constant because definite integration involves summing up infinitely many rectangles, each representing an infinitesimal change in the variable we're integrating with respect to. However, if we were to integrate with respect to a constant, there would be no possibility of infinitesimal change because the constant remains constant by definition. Therefore, we wouldn't be able to conform to the intrinsic properties of definite integration, making integration with respect to a constant impossible.
I have to say: - The first one is crazy awesome. - The second one is as fast with Substitution. - The third one is obvious for me as physics student. But only because we always use this and in maths course they proofed it, but I consider it logic.
The second one is a fun trick, but it is usually worse than substitution. It only simplifies things if you are lucky. In his example, replace the 4 with any other number and it doesn't actually make the problem any simpler. The fastest method (as long as you have the first few rows of Pascal's Triangle memorized) for that problem isn't any he mentioned, it's using the binomial theorem to expand.
@@generaldier1909 usually in the first semester you take calculus 1 where they teach you integral (much more advanced than school ) in the second sem you take calculus 2 where you heavily use integral and double integral , and in calculus 3 you use it but kinda less then calculus 1 and 2 , but you continue using integral in your whole degree and almost in every subject and you hate your life and you start searching for other major where there is no integral then its turn out that almost every technology , science , engineering major teach calculus 1 and 2 so you start hating you life more because you dont want to go the law school wish is almost the only degree with no calculus so eventually you force yourself to memorize every single integral and limits that ever existed and you finally pass the calculus exam after 10 years of studying maths but you realise that you waste your life and you wont even use it in your life ... so yeah i feel sorry for you and for the humanity because such a subject destroying people lives
The first is prooving by doing u-substitution with inverse f and do integration by parte. The second is prooving by doing u-sub with (a+b-x). The third is by doing a line integral over a vector function , where "k" is your parameter. Then you express this integral as a double integral from x = [a,b] and y = [k, inverse of F(0)]. If you take the partial of y in the double integral, you end up with F(b,k) - F(a,k), which is correct. "F" is the function integrated only with respect to x.
Sir, Third technique is ‘Feynman Integration Technique’ and it can also be generalized for nth derivative. But I have a question, Can first technique be used in complex integration?
They ate not writing backwards. Think logically. They made a video where they are writing normally and that makes the text backwards to us. But they edit the video such that it becomes laterally inverted. That is why he is writing with his left hand.
The first is prooving by doing u-substitution with inverse f and do integration by parte. The second is prooving by doing u-sub with (a+b-x). The third is by doing a line integral over a vector function , where "k" is your parameter. Then you express this integral as a double integral from x = [a,b] and y = [k, inverse of F(0)]. If you take the partial of y in the double integral, you end up with F(b,k) - F(a,k), which is correct. "F" is the function integrated only with respect to x.
I'm a Teacher... Nice tricks!! The last one is known as "Feynman's integral trick", or, more accurately, the "Leibniz rule"... It transform the original problem of calculating an integral in a different one of calculating a differential equation...
I suspect that they are not exactly the same and that you need both. If I understand correctly, the "Leibniz rule" is what Brian stated as "the trick", but in reality the "trick" is to parametrise the given integral using y so that applying Leibniz rule will give something doable, and this part is "Feynman's integral trick".
@@MichaelRothwell1 Feynman said himself that he took the so called "Feynman's trick" from a book (Wolf??) explicitly from the "Leibniz rule for differentiating under the sign of derivative"...
There is a reason why a lot of teachers won't tell you. Apart from the fact that not all teachers may know these tricks, there is only so much time available to teach the calculus curriculum. And typically there is a great time constraint. I teach calculus to oncoming engineers and if we have couple of snow days, I have a serious problem. I don't want students to drop either so there is no room to do the extra "fun" stuff. In those rare opportunities when I do have extra time AND if I happen to have a strong batch, I pick the second "trick" to teach. But ever since Corona started...forget it
If u dedicate 3-4 minutes per lesson period it might just work for a trick per lesson. This man did 3 in 11 mins 25 secs😅 just being an advocate for those brighter ones😁
@@truescalefpv4089 The time allotted is very different when you are teaching something for the first time. Here everyone knows how to differentiate by parts. When this would be taught in class, it would take students far more time to get up to speed, and during the unit on techniques of integration, they are already tapped out on all the different techniques and their nuances. I can guarantee you, it would not be 3 or 4 minutes.
Thanks a lot for your video. If one day I have to solve one integral for my work purposes, I will save a lot of time. Do not hesitate to post such videos with tricks if you have more.
Way to understand and remember the first one: use areas. The integral is the area bounded by the inverse of f with x axis. It is = area of rectangle - area subtended with y axis. The rectangle I mentioned has opposite vertices (0,0) and (x, finverse(x)). The sides are parallel to coordinate axes. Area is length × breadth. The area of inverse function bounded by y axis from y=0 to y= finverse(x) can be found as area of f bounded by x axis from x=0 to x= finverse(x). Because inverse function and f are symmetric about x=y.
I was blown by this... Really I have never seen such useful tricks before while I have studied a good bit of differentiation and integrals as a 12th grade student
How to write a single equation. (a+b) = 0 (a-b) = 0. Then ( a^2 - b^2) = 0. Similarly you can write it different forms. The first is atomicity. The second type is linkage. The third is generic. And there are so many other types. The more the different types of variable the more the types of turing machines.
Question: at 9:55 he plugs in one to the initial integrand and he says it's zero but strictly speaking wouldn't he have to use low L'hopital's rule because the denominator, lnx, is also zero at x= 1?
1 was really a shortcut ... it was just by parts in tricky manner .....understandable😊 2 was celeb I mean ..It is famous ...mentioned in many books🙂 3 was crazy and I just want to use it 😐😐😐👍
None of what you say is true. Since both x^5 -1 and lnx are negative at (0,1), their quotient is positive. Furthermore, it reaches a well defined limit at the endpoints and it's continuous throughout the interval, hence the improper integral is convergent.
Hey, Excellent video and amazing tricks! :D I have some questions: In the first trick Does it work for any inverse function? The second trick only works for polynomial functions(x^n) or whatever function? And finally, in the third, How do I know what number i have to change by another variable? ("y" in this case, "5" changed by y)
The first trick works with any inverse so long as you will be able to end up integrating it. The second trick will work for any function so long as it's defined for the appropriate values. For the third trick, I don't know if there is one way that will always work, sometimes it might be obvious and sometimes you might just have to try some different ways. I hope that helps!
The third trick is a thinking trick that was developed by Leibniz and popularized by Richard Feynman. Essentially what you want to do is, if you are clever enough, find the solution to a more general problem that involves your specific integral. Then you can find the answer. But you cannot use it for indefinite integration. Another example is the Dirilecht integral: Ssinx/xdx
The trick you describe at 4:14, is there particular occasions when that one is useful? What about when the sum of of the integration limits does not help eliminate any of the term within the expression?
How do i diffrentiate and integrate when it comes to triple difrrentiation of surface integrals and volume integrals by Feynman Technique and Riemann Technique ?
I'm an integral-aholic, anyone got suggestions on where I could learn more advanced integration techniques? Maybe even for different kinds of integrals?
If you have mastered all the fundamental techniques, it is time for you to spontaneously explore new options and set up your own substitutions and then follow your established paradigm. Try operations that may even appear seemingly counterproductive. Many great mathematical discoveries are found by going off the beaten path, doing something "counterproductive" or "weird.". It often makes incredibly difficult problems extremely easy by contradictorily complicating the situation. As an example do the following integral: 1/ (x^4 + x^3). When you set up your substitution, let u = (1 + x^-3) but first factor x^4 out of the denominator's sum to give you the u listed above and then take the quartic x to the numerator as a negative exponent, and it falls out like 🪄 - magic. Good luck and enjoy your journey and exploration of what mathematics really is!
By the way, search for "blackpenredpen" and "100 integrals" here on RUclips. That page's author did a 100 problems and has a worksheet with the solutions in the video description.
@@epicm999 Reach out to me for further guidance. You should try to develop "trailblazing" techniques. That is look to innovatively solve the integrals in question. Ask yourself, What other techniques or substitutions could I try? Try stuff out. You will find ways that are far more efficient than what we learned in school. With integrals, the proof is in the pudding because you can always check your answer by taking the derivative. Good luck and Google problem sets. You will find them.
thankyou so much 😀😀 these three formula really amazed me (can you also give the proof of these formula) and please make more vedio on secret formula of integration(which doesn't teach in school)
Did you know that the integral from -a to a of f(x) dx is equal to the integral from 0 to a of f(x) + f(-x) dx ? Did you know that the integral from 0 to +inf of f(x)/x dx is equal to the integral from 0 to +inf of the Laplace transform of f(x) taken over ds. Did you know that the integral from -inf to +inf of f(x) dx is equal to the integral from -inf to +inf of f(x - a/x) dx, for any real a. Though I dont know if there are restrictions on this rule. Id love to see more videos on cool integration techniques.
They ate not writing backwards. Think logically. They made a video where they are writing normally and that makes the text backwards to us. But they edit the video such that it becomes laterally inverted. That is why he is writing with his left hand.
Can you please tell me how to solve integrals using Laplace transformation . I don't know that much about it but I know one thing that it is used to calculate differential equations . But how to solve integrals ?
hi When you decide to replace a part of the integrand with y, what is your thought process? I find it a little hard to understand. Thanks a lot for this video :)
well you want to identify the part of the original integral that is troublesome-the part that sucks basically in that integral we hate having lnx in the denominator so we want to substitute(or multiply in certain cases) with something that would cancel lnx another classic example is the integral of sinx/x if you set a function f(t)=sintx/x and do the trick differentiating with respect to t you get the integral of xcostx/x and the x's cancel out and then you proceed as shown in the video that's why i said you multiply sometimes
It is actually a form of integration by parts since differentiation and integration are inverse operations. This is why inverse functions and the solution to a component integral are involved.
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🎓Become a Math Master With My Intro To Proofs Course! (FREE ON RUclips)
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wow! 0:48 how long did it take you to learn how to write in reverse?
it looks like you're writing on a plate of glass with the camera on the far side of it.
😊 very cool effect. (and cool maths too but that "goes without saying")
i'm teaching myself calculus, indirectly making you my teacher, meaning my teacher _has_ taught me these integral tricks
Good luck!
Wholesome
@Timon Fullbrook Year 12 why not
@@thepuzzlemaker2159 why not not?
LESS GOOOO
Actually you can integrate inverse functions by integrating original functions and subtracting it from the area of rectangle formed by the integration limit, it works because inverse of functions are symmetric about x=y line.
I didn't quite understand this method could you explain more
@@zaidabbassi6598 same. 😭
Genius
@@Sacchidanand
g(x) is inverse of f(x) .
integral of g(x) from a to b = a*b - integral of f(x) from a to b.
@@chromaxetian496 i tried this with e^x and ln x and it didn't work?
“By simply considering the differentiating with respect to 5, we can easily solve this problem!”
Can we integrate wrt to a const?
@@deekshanaik2438 no.
@@deekshanaik2438 No,we can't integrate with respect to a constant because definite integration involves summing up infinitely many rectangles, each representing an infinitesimal change in the variable we're integrating with respect to. However, if we were to integrate with respect to a constant, there would be no possibility of infinitesimal change because the constant remains constant by definition. Therefore, we wouldn't be able to conform to the intrinsic properties of definite integration, making integration with respect to a constant impossible.
Differentiation under the integral sign is a powerful method. Making a problem easier to solve by making it more complicated or more general.
Well said!
@@BriTheMathGuy I really enjoyed that video. Thanx
the first trick is basically 'integration by parts' treating 1 as first function
I have to say:
- The first one is crazy awesome.
- The second one is as fast with Substitution.
- The third one is obvious for me as physics student. But only because we always use this and in maths course they proofed it, but I consider it logic.
The second one is a fun trick, but it is usually worse than substitution. It only simplifies things if you are lucky. In his example, replace the 4 with any other number and it doesn't actually make the problem any simpler. The fastest method (as long as you have the first few rows of Pascal's Triangle memorized) for that problem isn't any he mentioned, it's using the binomial theorem to expand.
Which grade you are reading
@@generaldier1909
Me? At the end of physics Bachelor
At Which grade you have learn integration at first.
@@generaldier1909 usually in the first semester you take calculus 1 where they teach you integral (much more advanced than school ) in the second sem you take calculus 2 where you heavily use integral and double integral , and in calculus 3 you use it but kinda less then calculus 1 and 2 , but you continue using integral in your whole degree and almost in every subject and you hate your life and you start searching for other major where there is no integral then its turn out that almost every technology , science , engineering major teach calculus 1 and 2 so you start hating you life more because you dont want to go the law school wish is almost the only degree with no calculus
so eventually you force yourself to memorize every single integral and limits that ever existed and you finally pass the calculus exam after 10 years of studying maths but you realise that you waste your life and you wont even use it in your life ...
so yeah i feel sorry for you and for the humanity because such a subject destroying people lives
This us the first time feynmans trick made sense to me! Thank you!
These trick are real timesavers! Now im flying through every integral!
I suggest that you provide the original method then compare it with the hack. That way it would be much easier to understand and know if its credible.
Yes, and proof
The first is prooving by doing u-substitution with inverse f and do integration by parte.
The second is prooving by doing u-sub with (a+b-x).
The third is by doing a line integral over a vector function , where "k" is your parameter. Then you express this integral as a double integral from x = [a,b] and y = [k, inverse of F(0)]. If you take the partial of y in the double integral, you end up with F(b,k) - F(a,k), which is correct.
"F" is the function integrated only with respect to x.
last one was *absolute* *beast* .....
Thank you very much! Your presentation is clear and concise and very informative. You are an excellent teacher.
Glad it was helpful!
Sir,
Third technique is ‘Feynman Integration Technique’ and it can also be generalized for nth derivative.
But I have a question,
Can first technique be used in complex integration?
Probably not, why don't you try it on a few complex functions using wolframalpha?
Leibniz is the original inventor, Feynman popularised it!!!
the writing backwards makes this ten times as special and effort-filled. Nice video
Glad you thought so. Have a great day!
They ate not writing backwards. Think logically. They made a video where they are writing normally and that makes the text backwards to us. But they edit the video such that it becomes laterally inverted. That is why he is writing with his left hand.
@@TheLighthouse121 rwhoosh
@@ItamiPlaysGuitar r whoosh
@@ItamiPlaysGuitar
You need therapy
3:40 we call this the "king rule" for a reason
Thanks, Feynman's Integration technique is much clearer now.
The second trick was made by a maths legend from india the trick's name is 'King rule'.
Not only in india but around the world its known as the king rule
I bet that dislike was a teacher 😂
Hahahaha
Beautiful laura
😂
😂
Make the 66 teachers
5:35 ahh, the old Feymann integration technique
Ya
Didn't feynman also just stumble upon it while self learning calculus from an old book?🤔
@@anikmandal9900 Yes, book by Woods (I've forgotten his name) given to Feynman by his teacher
Papa flammy's gonna be mad
@@anikmandal9900 I think it was originally invented by leibniz
For those of you wondering about how to prove the first integral, substitute x=f(t) and use IBP
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
Fun fact: my teacher taught the whole class these. 3 and many more tricks 3rd trick is called Lebinitz 2nd rule of differentiation of integral
What other tricks did you learn?
average jee aspirant 🗿
The first is prooving by doing u-substitution with inverse f and do integration by parte.
The second is prooving by doing u-sub with (a+b-x).
The third is by doing a line integral over a vector function , where "k" is your parameter. Then you express this integral as a double integral from x = [a,b] and y = [k, inverse of F(0)]. If you take the partial of y in the double integral, you end up with F(b,k) - F(a,k), which is correct.
"F" is the function integrated only with respect to x.
I'm a Teacher... Nice tricks!! The last one is known as "Feynman's integral trick", or, more accurately, the "Leibniz rule"...
It transform the original problem of calculating an integral in a different one of calculating a differential equation...
I suspect that they are not exactly the same and that you need both. If I understand correctly, the "Leibniz rule" is what Brian stated as "the trick", but in reality the "trick" is to parametrise the given integral using y so that applying Leibniz rule will give something doable, and this part is "Feynman's integral trick".
@@MichaelRothwell1 Feynman said himself that he took the so called "Feynman's trick" from a book (Wolf??) explicitly from the "Leibniz rule for differentiating under the sign of derivative"...
@@breakingmath1 Fair enough, thanks!
I think a better interpretation is transform a line integral in a double integral
I'll never remember these tricks but glad I saw them ...
2:53 that's the hypotenuse side
There is a reason why a lot of teachers won't tell you. Apart from the fact that not all teachers may know these tricks, there is only so much time available to teach the calculus curriculum. And typically there is a great time constraint. I teach calculus to oncoming engineers and if we have couple of snow days, I have a serious problem. I don't want students to drop either so there is no room to do the extra "fun" stuff. In those rare opportunities when I do have extra time AND if I happen to have a strong batch, I pick the second "trick" to teach. But ever since Corona started...forget it
If u dedicate 3-4 minutes per lesson period it might just work for a trick per lesson. This man did 3 in 11 mins 25 secs😅 just being an advocate for those brighter ones😁
@@truescalefpv4089 It depends on the audience to what extend I can step outside the boundaries of curriculum
@@truescalefpv4089
The time allotted is very different when you are teaching something for the first time. Here everyone knows how to differentiate by parts. When this would be taught in class, it would take students far more time to get up to speed, and during the unit on techniques of integration, they are already tapped out on all the different techniques and their nuances. I can guarantee you, it would not be 3 or 4 minutes.
I have used the 2nd one so much... we call it king's property
Me, a calculus teacher watching so I can teach my students the tricks
Thanks a lot for your video. If one day I have to solve one integral for my work purposes, I will save a lot of time. Do not hesitate to post such videos with tricks if you have more.
5:22 how do you evaluate from 1-3 at this point?
Way to understand and remember the first one: use areas. The integral is the area bounded by the inverse of f with x axis. It is = area of rectangle - area subtended with y axis.
The rectangle I mentioned has opposite vertices (0,0) and (x, finverse(x)). The sides are parallel to coordinate axes. Area is length × breadth.
The area of inverse function bounded by y axis from y=0 to y= finverse(x) can be found as area of f bounded by x axis from x=0 to x= finverse(x). Because inverse function and f are symmetric about x=y.
It would be interesting a proof of all these tricks... 🧐
I knew the 2nd one, but 1st & last one were like from other planet. I never saw them. These are really good methods. Thank you for sharing.
You're welcome 😊
I was blown by this... Really I have never seen such useful tricks before while I have studied a good bit of differentiation and integrals as a 12th grade student
Very helpful
Love from India!!!
Glad you liked it!
How to write a single equation. (a+b) = 0 (a-b) = 0. Then ( a^2 - b^2) = 0. Similarly you can write it different forms. The first is atomicity. The second type is linkage. The third is generic. And there are so many other types. The more the different types of variable the more the types of turing machines.
6:20 i know this really well, it’s ln|s+1|
Nice!
Senior man, you are extremely intelligent.
I have noticed it.
I send your aza
When you get a 7 on your IB exam because of this guy
Thanks for your videos. I like them a lot, especially those with Tricks. As a suggestion may be to add it to the Calc 1playlist.
Thanks very much! I took your advice and added it to the playlist :)
Question: at 9:55 he plugs in one to the initial integrand and he says it's zero but strictly speaking wouldn't he have to use low L'hopital's rule because the denominator, lnx, is also zero at x= 1?
1 was really a shortcut ... it was just by parts in tricky manner .....understandable😊
2 was celeb I mean ..It is famous ...mentioned in many books🙂
3 was crazy and I just want to use it 😐😐😐👍
Any JEE Advanced aspirant watching it...?
Yoooo
😅
Jee advanced aspirant only memorizes worked out problems. No theory. 😂
Regarding the example of differentiation under the integral sign... the integrand is negative for for 0
Great point!
None of what you say is true. Since both x^5 -1 and lnx are negative at (0,1), their quotient is positive. Furthermore, it reaches a well defined limit at the endpoints and it's continuous throughout the interval, hence the improper integral is convergent.
Love you from India
Wow, five years ago, this Bri guy was a normal person. How things change.
Me watching this near the end of my maths degree crying that I've never seen these tricks before
Could someone explain to me how he recorded his video?
Because the camera didn't show the mirror image of what he was writing.
Maybe he's writing backwards on a clear pane of plastic between him and the camera?
I already knew the last one but it’s definitely the coolest one in my opinion.
Thanks Brian . Very helpful trick to apply on a test .
Glad it was helpful!
Yes we want more like this......
Could you please show harder examples using these methods. Thanks.
first trick is cool...but it can be done way more easily with integration by parts, taking arccosx as u, and dx as v'
It is easier if you know what the derivative of arccosine is! 🤣
Great Efforts...!!!
I love it
Appreciated!
*u earned an instant subscription*
Thanks!
my teacher skipped whole integration Chapter which was consist of Approx 25-35 marks of maths paper
I dont find thé vidéo of the 7 derivative tricks !
the last integral is divergent because 1/lnx is not continuous in 0 (i think)
No.
Hey, Excellent video and amazing tricks! :D
I have some questions:
In the first trick Does it work for any inverse function?
The second trick only works for polynomial functions(x^n) or whatever function?
And finally, in the third, How do I know what number i have to change by another variable? ("y" in this case, "5" changed by y)
The first trick works with any inverse so long as you will be able to end up integrating it. The second trick will work for any function so long as it's defined for the appropriate values. For the third trick, I don't know if there is one way that will always work, sometimes it might be obvious and sometimes you might just have to try some different ways. I hope that helps!
The third trick is a thinking trick that was developed by Leibniz and popularized by Richard Feynman. Essentially what you want to do is, if you are clever enough, find the solution to a more general problem that involves your specific integral. Then you can find the answer. But you cannot use it for indefinite integration. Another example is the Dirilecht integral: Ssinx/xdx
Luis M same thing
I had 1 teacher that hate us if we used DI method because too obsessed with the "original way"
I need more examples to solve for training. very interesting method!
Thank you soo much. It helped a lot. I loved that second trick, canceling 4
Glad it helped!
By your name, I'm guessing you're Indian, we use that method as a standard method in NCERT
@@marvel.studios Oh that's soo cool I am in class 11 ryt now
@@marvel.studios I know that hahaha, it is cool 🤣😅
@@b.h.shashaank8713 your in 11th then why are you watching this video 😂
Knew the second and third tricks(theorems) .thanks for the first one
bro you saved me
thank you for life
that last trick is godsent
Feynman technique 5:54
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
2:53 you mean hypotenuse?
Yes
It took me two tries but I understood them all completely :) thanks
Thanks sir!
Most welcome!
I don't know how you are writing in reverse with left hand.
Thank you for explaining..
The trick you describe at 4:14, is there particular occasions when that one is useful? What about when the sum of of the integration limits does not help eliminate any of the term within the expression?
Great job brother!
Thank you! Cheers!
Can I find the proofs of these anywhere?
Derivative trick that teachers won't tell you!
ruclips.net/video/BjDsJUkDsY4/видео.html
Thank youuuu ❤️
I'm in 12th standard studying in CBSE board, we use the second technique EXACTLY the way you explained it, as standard
Same, I’m in isc
Kings property
How do you prove the first one? My teacher wants me to prove it before using it :)
3:49 good ol' kings rule
What book can you suggest for self-studying differential equations?
book from Richard D Prima
what is arc cosinx ?? i mean i know basic trig , but never heard of arc !
Awesome stuff
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐💐
more easily, cos^2(x) + sin^2(x) = 1 so sin(x) = √(1-cos^2(x)) and sin(arccos(x)) = √(1-cos^2(arccos(x))) = √(1-x^2)
Thank you ♡
Welcome!
How do i diffrentiate and integrate when it comes to triple difrrentiation of surface integrals and volume integrals by Feynman Technique and Riemann Technique ?
I'm an integral-aholic, anyone got suggestions on where I could learn more advanced integration techniques? Maybe even for different kinds of integrals?
Follow Hallie Black on Quora :)
If you have mastered all the fundamental techniques, it is time for you to spontaneously explore new options and set up your own substitutions and then follow your established paradigm.
Try operations that may even appear seemingly counterproductive. Many great mathematical discoveries are found by going off the beaten path, doing something "counterproductive" or "weird.". It often makes incredibly difficult problems extremely easy by contradictorily complicating the situation.
As an example do the following integral:
1/ (x^4 + x^3). When you set up your substitution, let u = (1 + x^-3) but first factor x^4 out of the denominator's sum to give you the u listed above and then take the quartic x to the numerator as a negative exponent, and it falls out like 🪄 - magic.
Good luck and enjoy your journey and exploration of what mathematics really is!
By the way, search for "blackpenredpen" and "100 integrals" here on RUclips. That page's author did a 100 problems and has a worksheet with the solutions in the video description.
@@mathematix-rodcast Thank you so much!
@@epicm999
Reach out to me for further guidance. You should try to develop "trailblazing" techniques. That is look to innovatively solve the integrals in question. Ask yourself, What other techniques or substitutions could I try? Try stuff out. You will find ways that are far more efficient than what we learned in school. With integrals, the proof is in the pudding because you can always check your answer by taking the derivative.
Good luck and Google problem sets. You will find them.
Thanks 👍👍👍
From INDIA.....
Welcome!
thankyou so much 😀😀 these three formula really amazed me (can you also give the proof of these formula) and please make more vedio on secret formula of integration(which doesn't teach in school)
I really want more is very interesting
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
Did you know that the integral from -a to a of f(x) dx is equal to the integral from 0 to a of f(x) + f(-x) dx ?
Did you know that the integral from 0 to +inf of f(x)/x dx is equal to the integral from 0 to +inf of the Laplace transform of f(x) taken over ds.
Did you know that the integral from -inf to +inf of f(x) dx is equal to the integral from -inf to +inf of f(x - a/x) dx, for any real a. Though I dont know if there are restrictions on this rule.
Id love to see more videos on cool integration techniques.
They ate not writing backwards. Think logically. They made a video where they are writing normally and that makes the text backwards to us. But they edit the video such that it becomes laterally inverted. That is why he is writing with his left hand.
ruclips.net/video/XQIbn27dOjE/видео.html 💐👍
You are right bro
Awesome...first one is awesome...and last one is Feynman's Method of integration...and we can also use Laplace transform for solving this
Very cool! Thanks for watching and have a great day!
@@BriTheMathGuy yes... it's really nice...love your videos...
Kazi Abu Rousan thank you very much!
This is also the Leibniz rule for integration
Can you please tell me how to solve integrals using Laplace transformation . I don't know that much about it but I know one thing that it is used to calculate differential equations . But how to solve integrals ?
If I write ans straight I won't even get 0.5 marks but this is helpful to check answers easily
Faynmann's technique should be thought in calculus lessons ngl (to those who do not know 3 tricks)
hi
When you decide to replace a part of the integrand with y, what is your thought process? I find it a little hard to understand. Thanks a lot for this video :)
ruclips.net/video/XQIbn27dOjE/видео.html 💐💐
well you want to identify the part of the original integral that is troublesome-the part that sucks basically
in that integral we hate having lnx in the denominator so we want to substitute(or multiply in certain cases) with something that would cancel lnx
another classic example is the integral of sinx/x
if you set a function f(t)=sintx/x and do the trick differentiating with respect to t you get the integral of xcostx/x and the x's cancel out and then you proceed as shown in the video
that's why i said you multiply sometimes
Where did the first one come from and how do you derive it?
It is actually a form of integration by parts since differentiation and integration are inverse operations. This is why inverse functions and the solution to a component integral are involved.
Thanks 😊
IIIIIIIIIII. I enjoyed it!!!!!! Love it!!!!!👌👌👌
I'm gonna put it in my playlist...
Great to hear! Thanks for watching and have a nice day!
BriTheMathGuy Thanks! Keep doing great job.
I already used this formulas! In my 10th grade ✨💫
That's great!
7:27 that is feynman trick