Integral of the Day 8.26.24 | Substitution AND By Parts! | Calculus 2 | Math with Professor V

Here's your latest Integral of the Day! Hope you enjoy! Did you solve it differently? Comment down below!

Don't forget to LIKE, Comment, & Subscribe!

xoxo,
Professor V

Calculus 2 Lecture Videos on Integration:

Trig Review:

Calculus 3 Video Lectures:

#mathwithprofessorv #integration #partialfractions #partialfractionmethod #partialfractiondecomposition #trigonometricsubstitution #trigintegrals #trigsubstitution #integrals #integralcalculus #calculus2 #calculusvideos #calculus2videos #integralvideos #trigonometricintegrals #math #youtubemath #mathvideos #mathtutor #mathprofessor #calculusvideos #integrationbyparts #integralcalculus

Join this channel to get access to perks:

Socials:
IG: @mathwithprofessorv
TikTok: @mathwithprofessorv

I'm also an Amazon influencer, so feel free to support and shop:

EXCITING NEWS: You can now sign up for my Patreon at the link below!

My Patreon is a place for students to have access to exclusive ad-free content not available on my YouTube channel! Access to the library of additional videos, worksheets, and more is available with the "Star Pupil Package" tier for just $9.99/month (USD).

*This video is copy protected and cannot be downloaded or used in any capacity without my permission.*

[siyabongashoba]

Dear Prof.V I hope you are doing well, For this one I used integration by part two time, u = sin(lnx) ;du=cos(lnx)*1/x dx and dv=dx ; v = x and the output = xisn(lnx) - integral of cos(lnx)dx. for the cos(ln(x)) I apply integration by part p = cos(lnx) ; dp = -sin(lnx)*1/x dx ;dm=dx ; m = x it output xcos(lnx) + integral of sin(l`nx)dx which is repeating you told me like that so the final was 1/2 * xsin(lnx) - 1/2 * xcos(lnx) + C let me enjoy the video.

[tonychow]

Hi Professor V, thank you for your new video. I used the same method as yours, but I took u=e^t and v=sintdt. The result was the same. Cheers.

[siyabongashoba]

wow t = lnx, the one and only Prof.V, never think that can come out outstanding like that. thank you so much

[danny]

I did it a little differently! I used IBP and set u = sin(lnx) and dv = dx, and then got xsin(lnx) - the integral of cos(lnx), and then i did IBP again with the new integral which gave me another integral of sin(lnx), and then i solved for the integral of sin(lnx) and got the same answer

[AndrewJohnson-urlw]

When doing multiple IBP I suppose that the DI method favoured by others would have perhaps looked better