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 Integration - Video Lessons: www.video-tutor.net/integration-techniques.html

[@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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[@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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[@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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