Little help? simple problem

1. Dec 20, 2007

ricekrispie

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
i know it´s supposed to be simple but it is driving me nuts...

Integrate:
xlnx dx

thanks for helping

2. Dec 20, 2007

ice109

integration by parts, note pick your u and dv carefully

Last edited: Dec 20, 2007
3. Dec 20, 2007

mathman

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. Dec 23, 2007

martial

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 gotta do that last integral.