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Integrating a x^k ln(x) Function with Gamma Function
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[QUOTE="clandarkfire, post: 4494855, member: 398373"] It does seem pretty straightforward with integration by parts, but since I'm told to use the gamma function, I'd at least like to know how to do that. If I use the substitution [tex]x=e^{-u/k}[/tex], I get [tex]dx = -k*e^{-u/k}\,du[/tex] The integral then becomes [tex]\int^1_0 e^{-u}*-\frac{u}{k}*-k*e^{-u/k}\,du = \int^1_0 e^{-(u + \frac{u}{k})}u\,du[/tex], but the problem remains that it's between 0 and 1, not 0 and infinity. How do I get to a gamma function from there? Thanks! [/QUOTE]
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Integrating a x^k ln(x) Function with Gamma Function
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