Integral of (lnx)^2

This calculus video tutorial explains how to find the integral of (lnx)^2 using integration by parts.

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[secondjar]

I love how I think I am getting the hang of calc 2 and run into silly problems like this. It's one of those classes that seems deceptively easy at first and then slams you on your head.

[Understandablish]

Working on a Calc II assignment and found the concepts used to set up the problem extremely helpful for a more complex version. Thanks for doing what you do!

[charlesdicus]

thank you sir. there are a lot of non obvious integrals that help you solve a breadth of problems that youve shown me.

[elnurs]

Thank you for showing these specific examples 👌

[helloworld-hi]

I solved the problem by choosing the inverse log aka e^x and let x = e^t and lnx = t
So dx = e^t dt
Now we are integrating t²e^t dt
Results in t²e^t - 2te^t + 2e^t + C using the Tabular Method.
We know, t=lnx
So the integral of lnx^2 dx = xln²x - 2xlnx + 2x + C
And results in the same answer! 🙂

[Fish-DDD]

You are the best I learn almost everything from you🧘🏻‍♂️👑

[WiseSnake]

Man getting me through the last quarter of Survey of Calc.

[maivy]

Dude thank you so much. I have been trying to solve this problem, but I can't Soo thank you Soo much again

[bigl]

what a boss man I love this guy. what a cool guy

[idkwhattodo.....]

U can put lnx=t, then dx=xdt and x can be written as e^t
Overall the integration is t².(e^t)dt

[mattybatten]

why cant we just integrate (lnx)^2 by reverse chain rule?

[juliak]

Hiii, can you explain why integration by parts is used here? My first thought was to integrate by substitution with u= lnx as sub

[Darapureddysaikumar]

my first idea looking at the problem is u substitution why can't we use it can anyone explain it

[tpzlol]

Thanks but the similarity of u and v in your handwriting makes this unnecessarily confusing

[carlosseroya]

Godamn I never thought of it that way. Thanks so much

[tylermacdonald]

Why the fuck is the sign of integration suddenly a factor in the integral? How does this work at all? I am so confused.

[RadKnight]

0:56 you took dedicate of u here but after that you took integration of v whys that

[maxwellvargas]

when I use derivative on the result, it gives me 2dx. why though?

[naseemgharibi]

thank you for your work
can i please ask why did you put 2 in front of the second integral in 2:53 ?
i mean the first integral has the 2 already but why you did put it again ?
thanx again :D