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

  • Thread starter ricekrispie
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In summary, the person is a high school senior studying AP Calculus BC and is trying to figure out integration by parts, specifically with the problem of integrating xlnx. They are seeking help and have been advised to choose u and dv carefully, with a hint to consider d(ln x)/dx = 1/x. They have been given two options for u and dv and are advised to choose the one that will be easier to handle. The final step is to complete the integral by solving for the last integral.
  • #1
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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  • #2
integration by parts, note pick your u and dv carefully
 
Last edited:
  • #3
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.
 
  • #4
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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