Integral of lnx

This calculus video tutorial explains how to find the integral of lnx using integration by parts.
Calculus 1 Final Exam Review: • Calculus 1 Final Exam ...
Integration - Formula Sheet: bit.ly/3XCT6oz
Full-Length Exam Videos: / mathsciencetutor
Calculus Video Playlists: www.video-tuto...
_______________________________________________________________________________________
Integration & Antiderivatives: • Calculus 1 - Integrati...
Calculus 1 - Derivatives: • Calculus 1 - Derivatives
Integral of 1/Sqrt(x): • Integral of 1/sqrt(x)
Integral of |x|: • Integral of absolute v...
Integral of Cos(2x): • Integral of Cos(2x)
Integral of Cos^2(x): • Integral of cos^2x
Integral of Sin^2(x): • Integral of Sin^2x
Integral of Sin^4(x): • Integral of sin^4x
Integral of Tan^2(x): • Integral of tan^2x
_____________________________________________________________________________________
U-Substitution Integration: • How To Integrate Using...
Integral of 1/e^x: • Integral of 1/e^x
Integral of ln(x)/x: • Integral of lnx/x
Integral of 1/(1+e^x): • Integral of 1/(1+e^x)
Integral of Tan(x): • Integral of tanx
Integral of Sec(x): • Integral of sec(x)
Integral of Sin(x)Cos(x): • Integral of sinx cosx
Integral of x/sqrt(1-x^2): • Integral of x/sqrt(1-x^2)
Integral of x/sqrt(x+1): • Integral of x/sqrt(x+1)
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Integration By Parts Technique: • Integration By Parts
Integral of xe^x: • Integral of xe^x
Integral of e^x Sinx: • Integral of e^x sinx
Integral of ln(x): • Integral of lnx
Integral of (lnx)^2: • Integral of (lnx)^2
Integral of ln(x)/x^2: • Integral of lnx/x^2
Integral of ArcSin(x): • integral of arcsin(x)
Integral of e^[sqrt(x)]: • Integral of e^sqrt(x)
Integral of Sin(lnx): • Integral of Sin(lnx)
Integral of Sec^3(x): • Integral of sec^3x
_____________________________________________________________________________________
Trigonometric Integrals: • Trigonometric Integrals
Integral of Sin^3(x): • Integral of sin^3x
Integral of Sin^5(x): • Integral of sin^5(x)
Integral of Tan^3(x): • Integral of tan^3(x)
Integral of Tan^4(x): • Integral of tan^4x
Integral of Tan^5(x): • Integral of tan^5(x)
Integral of Cos^3(x): • Integral of cos^3x
_____________________________________________________________________________________
Trigonometric Substitution: • Trigonometric Substitu...
Integral of 1/(1+x^2): • Integral of 1/(1+x^2)
Integral of x^2/(x^2 + 1): • Integral of x^2/(x^2+1)
Integral of 1/sqrt(1-x^2): • Integral of 1/sqrt(1-x^2)

[@TheOrganicChemistryTutor]

Integration - Formula Sheet: bit.ly/3XCT6oz
Final Exams and Video Playlists: www.video-tutor.net/

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God just take me

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Us

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Frrrr I hate integrals😭😭😭

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Man's real frustrated

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HELL YEA BRO THIS IS WHAT IM TALKIN BOUT! ALL THESE OTHER CLOWNS ON RUclips TOOK 8 DAMN MINUTES TO EXPLAINS THIS. YOU COME OUT HERE AND JUST SHIT ON THEM WITH A MIRACULOUS 1:25 VIDEO THAT WRECKS THESE DUDES MAN. HELL YEA YOU ARE GETTING ME THROUGH USAFA MAN HELL YEA. ALL HAIL ORGANIC CHEMISTRY TUTOR!

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[@reza9417]

Thanks, now i understand

[@_Xypes_]

I don’t but at least I know the solution

[@alexts94]

@@_Xypes_ It's simple, if u is ln(x), then dv is just 1 (times dx). He didn't make it clear that the constant for dv was 1, but that's what was implied here

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Thanks 😊
Keep up the good work 👍🏻

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Very helpful
Thanks
Good day

[@tylang9357]

is 'v' really necessary then? if 'x' = 'v' then why not just state 'x' from the start

[@NotSoChillBozo]

Rather than treat it as a question, treat it like an example of using the udv method!
Comparison really helps make things clear and you can apply the rule to other complex ones!

[@chris5207]

so basically we treat it as 1x lnx and integrate the 1 to x - nice

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[@jonathanyork597]

For those wondering: This is a caculus 2 method (or AP Calculus BC). I was originally confused as well lol

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[@xa-dienn8172]

bu kadar kolay beklemiyodum. iyiymiş.

[@gabe5225]

My math teacher after I say integral of ln(x) = 1/x:

[@jeffthegamerboy3476]

1/x is the derivative of ln(x), not it's integral!

[@jamesojajuni7627]

If I differentiate the answer, I get "lnx - 1" instead of lnx

[@calvynmoungoungou8688]

Before we get to that what did you get when you differentiated x ln x

[@AldousSeriousPunch]

d/dx (x ln x - x)
= (ln x)(1) + (x)(1/x) - 1
= ln x + 1 - 1
= ln x

[@sophiahxazz8750]

so good, thk u

[@user-hv6ef9ie1g]

0:40 I still don't understand why we should pick dx for dv (dv=dx) instead of x for dv (dv=x) (since x is inside of ln)

[@heylyy]

From what I understand, dv = dx because there is an invisible 1 there so dv = 1 dx which makes v = x. the 1 comes from the main integrand 1*lnx, its just not shown explicitly. also i dont understand the point of picking x for dv since x is inside of ln since were using int by parts which is essentially the reverse product rule, i think what you meant by that is for u sub which is for composition of functions though correct me if im wrong.

[@jakepark7837]

You are thinking of the chain rule. Integration by parts is more like the product rule. It is for two functions that are multiplying that you want to integrate. ln is not multiplying x it is a function so you cant choose it for integration by parts.

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Ty

[@miko24858]

how about the integral of ln(cos x)?

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[@shankme6657]

can someone explain why DV here is dx.... i kinda dont get the logic of it bc in other examples, the dx isnt their DV.😢😢😢😢

[@Zeromarwins]

its actualy not and if you do it will be wrong dv = 1 v = x , u = ln(x) and du = 1/x try it out this way it will work if you dx = dv you will remove have no integration variable in the last part - integral of (vdu)

[@hk254lyt8]

Log has to be u since it takes priority so that forces you to choose dx as dv

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Yeah. I understand ☺️🙏.

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I should have watched this before putting a random answer on my paper 😭

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