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

[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

 

[ice109]

integration by parts, note pick your u and dv carefully

 

[mathman]

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

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.

 

[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 got to do that last integral.