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I'm having trouble with finding an improper integral.

The problem is ∫

^{1}

_{0}(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?

Thanks in advance!