Integration By Parts

[@TheOrganicChemistryTutor]

Integration - Free Formula Sheet: bit.ly/3XCT6oz Full 1 Hour 32 Minute Video: www.patreon.com/MathScienceTutor Direct Link to The Full Video: www.bit.ly/3zzzbZg

[@crt5866]

hey, quick question, when do you know to integrate by parts more than once? I have looked all over for the answer but I can't seem to figure it out.

[@pingpong3311]

@@crt5866 Usually when you have an x raised to a power in your integral.

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which school?

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[@tomasbeltran04050]

0:08 ex times e to the ex (x*e^x) power. 1:55 ex times sine of ex (xsin(x)) 3:30 ex squared times natural log of ex (x²ln(x)) 6:05 natural log of ex (ln(x)) 7:43 ex squared times sine of x (x²•sin[x]) 11:30 ex squared times e to the ex (x²•e^x) 14:55 the square of the natural log of ex (ln[x])² 17:26 natural log of ex to the seventh power (ln[x⁷]) 18:39 the product of e to the ex and sin of ex ([e^x]•sin[x])

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Thanks

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[@mokshcodes]

For the problem at 22:30, you could also use u-substitution to make u = lnx and du = l/xdx. Then, the integral would just be u squared du and the antiderivative would be (u cubed over 3) + C. By back substitution, you would get (lnx cubed over 3) plus C. This is just a quicker way to do the problem for time constraints on a test.

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[@devooko]

nicely noted

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I have more examples like this on my channel if you want more practice!

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The epiphany at 21:00 truly hit different after thinking about how to solve that integral for so long. All hail the organic chem tutor.

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Professor Organic Chemistry Tutor, thank you for an excellent video/lecture on Integration by Parts in Calculus Two. Integration by Parts is not a difficult process in Calculus; however, the problems can get long and messy and there is a fifty percent chance of making errors. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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did u fail

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[@IAmNumber4000]

Integration by parts makes me want to cry ;(

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I was just studying integration by parts for my exam an this notification poped in

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My high school teacher had some of these exact same questions and explained them completely wrong to the class. I was losing my mind trying to understand her notes until I found this video. Thank you

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Are you in a different country? Or in the US? How are you doing calc 2 in hs?

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@@blindyoutubeuser I’m in the U.S. currently. I’m a senior and Im ahead 2 years in math which is why I’m taking it in high school

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[@TheOrganicChemistryTutor]

You're welcome

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