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So I have a problem, which is to use integration by parts to integrate...

[tex]\int^{1}_{0}(1-x) ln (1-x) dx[/tex]

The way I have been working is it to seperate it out into just...

[tex]\int^{1}_{0}ln (1-x) dx - \int^{1}_{0}x ln (1-x) dx[/tex]

and then integrating by parts on each of these seperatele, but for instance if I integrate by parts the first bit, I get...

[tex][xln(1-x)]^{1}_{0} + \int^{1}_{0}x \frac{1}{1-x}[/tex]

And im thinking the first part to this doesn't make sense, because [tex]ln (0)[/tex] is a mathematical nono. So im confused with regard to this problem - has anybody any decent suggestions on how to do this?

Thanks :)