Solve the Integration by Parts Equation: xlnx dx | Senior in AP Calculus BC

  • Context: High School 
  • Thread starter Thread starter ricekrispie
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Discussion Overview

The discussion revolves around the integration of the function xlnx using integration by parts. Participants are exploring the method and sharing their approaches to solving the integral, which is a common topic in calculus courses.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant expresses difficulty with the integration by parts problem involving xlnx and seeks assistance.
  • Another participant suggests carefully choosing u and dv for the integration by parts method.
  • A later reply offers a specific choice of u = ln x and dv = x dx, providing the derivatives and suggesting a path to solve the integral.
  • There is a hint provided about the derivative of ln x, which may help in the integration process.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach, as different choices for u and dv are suggested without agreement on which is superior.

Contextual Notes

Participants have not fully resolved the integral, and there may be assumptions about the familiarity with integration techniques that are not explicitly stated.

ricekrispie
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hello.. i´m a hs senior in ap calculus bc but i went out of the country for vacations and brough my calculus book with me... i´ve been trying to figure out integration by parts by myself but i stumbled on this problem:confused:
i know it´s supposed to be simple but it is driving me nuts...

Integrate:
xlnx dx

thanks for helping :smile:
 
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integration by parts, note pick your u and dv carefully
 
Last edited:
ricekrispie said:
hello.. i´m a hs senior in ap calculus bc but i went out of the country for vacations and brough my calculus book with me... i´ve been trying to figure out integration by parts by myself but i stumbled on this problem:confused:
i know it´s supposed to be simple but it is driving me nuts...

Integrate:
xlnx dx

thanks for helping :smile:
You have two choices (u=x and dv=lnxdx) or (u=lnx and dv=xdx). Choose the one you think will be easier to handle.
 
Hint, d(ln x)/dx = 1/x...

Oh, whatever: u = ln x, dv = x => du = 1/x, v = x^2/2.
So you get (x^2 * ln x)/2 - Int(x/2, x). And you just got to do that last integral.
 

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