A-Level Maths: H5-12 Further Integration: Introducing Integration by Substitution

[gordonwoods]

Just wanna say that you are honestly getting me through A level Maths. Thanks so much!!!

[helenday]

I've noticed that some of the greatest Maths lessons (masterpieces of creating clarity and order from a confusing sea of detail) on YouTube often predict those little puzzlements that arise in your head (puzzlements that can be vital links in the chain of your understanding) and TL did that for me in this lesson.
That is, it occurred to me to ask myself HOW do you know WHEN to use the Integration by Substitution Rule?. I just couldn't think of what it was, by myself.
But then TL told us in this lesson how it's often appropriate to use it when you get something like (2x + 1)^5., which would take ages to integrate without the Integration by Substitution Rule. So helpful to know that.

[GCSEALevelMaths]

This is explained really well sir good job.

[jacksonsmith]

anyone else think his voice is so relaxing

[charliebrett]

As I struggle sometimes with reversing the chain rule Is it worth just always doing integration by substitution as I find it a lot easier? Also very dumb question but what does the dx actually mean and when you do the integral of (2x+1)^5 dx, what are you actually doing? Is (2x+1)^5 dx the derivative?

[lukeh]

thankyou so much you are so cool and such a good teacher

[LeeLarner]

Could you just use pascals triangle to expand the (2x+1)^5 and then once you have done with that integrate it using ax^n+1/n+1 or would that method not work

[ninanakagawa]

hi mr jack i'm sorry but could you solve my problem? (A+B) = 5π/6 sinAcosB= 1/3 find cot (A-B)

[AceOfHearts]

Hi Jack, thank you again for the vid. I just wanted to ask this question if I may. It may or may not be a common question, is u sub ALWAYS reversing the chain rule?

In the example you did, we could see the reverse rules there. But the the thing I want to get clear on, is that basically, I have found integrals I cannot reverse the chain rule, but somehow a u sub seems to solve it.

Like consider this one:

Integrand: 3x(x-4)^4... I could not see how chain rule could be reversed, but put, u=x-4 and crank the handle, VOILA... how does that work?

So just a bit confused whether it does reverse the chain rule in ways I dont know about or something else?

[amirbatayi]

Sth that my teacher taught for 2h and I still struggled, he taught me in 6 minutes if that’s not talent then what is it ?

[destined]

Why did du disappear after you have integrated ?

[blazethe]

Hi. I was doing a question where I had to integrate sqaure root of x squared + 4 and that over x. Initially I made the u as x squared +4 as that was the function inside the square root however u cannot do the question like that as u was meant to be square root of x squared + 4. I was gonna to ask is there a definite way of knowing what to make u? Or do you have to trial and error? Also I heard that for a level maths majority of the time u is given unless the question is easy, is that true ?

[youtuberue]

Do you have videos where you teach mechanics AQA instead of past papers? If you don’t do you have any other links you know that do mechanics 1 A Level AQA

[avoriginal]

The reverse chain rule gets you 12(2x+1)^6 whereas subs gets you 1/12(2x+1)^6, sm1 pls explain, or why does it get put into 1/12 at minute 1.55

[victory]

I can see what you do with the du/dx and how you substitute out the dx replacing it with 0.5du which you then use to multiply u^5 by 0.5, but I don't really understand why this can be done and how it works. I don't really understand what the dx at the end of every integral means and what the du at the end of this integral means. I assume it means (integrating) with respect to x or u, but I don't understand how you can have a half du, then multiply everything by a half and now you integrate properly? Maybe this is all unnecessary and I should just accept the rule.

[syedabbas]

How do you know when to use integration by parts or integration by sub?

[CrunchiestGranola]

Why can you just use the derivative like a fraction?