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How to Integrate ln(x)?
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- čas přidán 7. 08. 2024
- What is the integral of ln x? We apply integration by parts to solve this because it is a product of functions, where ln x multiply by 1 dx.
We first select ln x as 'u', and 1 dx as 'dv'. Then, we take the derivative of 'u' in terms of dx, and take the integral of 'dv'. Finally, plug them into the formula of integration by parts and we got ' x ln(x) - x + C ' as our final answer.
#integration #integral #calculus
INTEGRATION BY PARTS EXPLANATION: → • Integration By Parts F...
TIMECODES:
0:00 → Intro
0:13 → Why Integration By Parts is used?
0:34 → Selection of u and dv
1:15 → Derivative of u & Integral of dv
1:50 → Plug in the terms into formula
2:26 → We did it!
![How to integrate tan x? [2 Methods]](http://i.ytimg.com/vi/hrIS3rBSoIA/mqdefault.jpg)
![How to integrate tan x? [2 Methods]](/img/tr.png)
This is less commonly done and has higher prerequisites, but you could write out ln(x) as integral 1 to x of 1/t dt, and reverse the order of integration. You might have to set up the outer integral as a definite integral, such as int_1 to x of ln(s) ds, so you have a concrete region for Fubini to work with.
This definite form is an antiderivative of ln, with a specific "+C" built in, which you can rewrite in a simplified form with a generic +C absorbing any unnecessary constants when stating the general antiderivative we were looking for. I got a +1 I didn't need when I did this.
I have a question
My first thought is to use u sub. Let x=e^u, dx=e^udu Then we have integral(ln(x)dx)= integral(e^u*udu) and then integration by parts which clearly simplified because of exponential.
why not DI method
D I
+ lnx 1
- 1/x x
since -(1/x)(x) can be integrated stop there
then you get
∫lnx dx = xlnx - ∫(1/x)(x) dx
= xlnx - x + C
Yeah, that's true. DI method can also be used to get the answer. The one I've used here is just a normal IBP.
its the same process bro
DI method is just a way to write down IBP right? same thing.
Here it doesnt matter but sometimes it is good idea to choose a constant other than zero
when we calculate v from dv
Isn't it ILATE instead of LIATE
Hello, sorry, what software do you use to make this video?
I only use Microsoft PowerPoint as visual display, and Microsoft CLIPCHAMP as voiceover and merge it with the PPT slides.
Thank you🌹
@@icafe36485 You're welcome
Help me in his question Cos^3xdx by using integration by party
Why?
[ cos^(2)x][cosx]
[1-sin^(2)x][cosx]
Set your u=sinx
There is no needfor integration by parts
very nice Integral! can you please show me by another way?
Thanks! Another way to find the integral without performing integration by parts is to use the DI Method, in which we will still be getting the same answer.
oh! i got it.thanks sir!@@YeahMathIsBoring
integrate (x^n (lnx)^n )
J=xlnx-x+k
ln ❌️
lawn ✅️
Lol that AI VOICE IS CRACKING ME UP😂😂
It's voiceover generated from text by using MICROSOFT CLIPCHAMP.
@@YeahMathIsBoring ya Ik it's text to speech but the ai voice over kinda failed to pronounce word ln that's where It got me
@@godisalive6685 😂😂
You don’t need to say it’s lnx times 1 lol just let dv = dx
You're right! I was just intended to provide a better clarification and understanding.
@@YeahMathIsBoring right I know but I don’t think it does
dv is just the rest of what’s left over
Since IBP is taught as a method for integrating products of functions is good to mention it at least though
@@coreymonsta7505 Yup, cuz some might think that lnx is just a single logarithmic term and they're confused why IBP is applied here
Don't know how much you have to pay for AI voice, but you should consider switching even if you have to pay a bit more. Get an AI voice that knows a little math. "ln" is not "lawn" as in "mow the lawn". Once or twice might be charming but the whole video is about ln so "lawn" gets quickly annoying. Mike
That is how it is pronounced