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## Homework Statement

Not exactly a homework problem, but I noticed that wolfram alpha gives

[itex]\displaystyle{\int_{0}^{1}}x\ln{x}\,dx=-\frac{1}{4}[/itex]

I was wondering why this is so.

**2. Homework Equations & solution attempt**

For [itex]\epsilon>0[/itex]

[itex]\displaystyle{\int_{\epsilon}^{1}}x\ln{x}\,dx=-\frac{1}{4}-\left(\frac{1}{4}\epsilon^2(2\ln{\epsilon}-1)\right)[/itex]

Taking [itex]\epsilon \to 0[/itex] gives the answer provided by wolfram alpha.

My question is what justifies this last step of taking [itex]\epsilon \to 0[/itex]? Continuity?