# Finding Whether Improper Integrals Converge

Hi all,

I'm having trouble with finding an improper integral.

The problem is ∫10(xln(x))dx

My book says the answer is -1/4, but I do not understand how this is the case.

lim(xlnx) as x approaches 1- = 0

lim(xlnx) as x approaches 0+ = ∞

So how does this value converge at -1/4?