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How to evaluate this integral to get pi^2/6: 
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#1
Mar1612, 01:39 AM

P: 35

[itex]\int_0^\infty \frac{u}{e^u  1}[/itex]
I know that this integral is [itex]\frac{\pi^2}{6}[/itex], just from having seen it before, but I'm not really sure if I can evaluate it directly to show that. I know that: [itex] \zeta(x) = \frac{1}{\Gamma(x)} \int_0^\infty \frac{u^{x1}}{e^u 1} du [/itex] Does the value [itex]\frac{\pi^2}{6}[/itex] come from using other methods of showing the result for [itex]\zeta(2)[/itex] and solving the equation, or is that integral another way of evaluating [itex]\zeta(2)[/itex]? 


#2
Mar1612, 01:05 PM

P: 312




#3
Mar1712, 05:06 PM

P: 35

Anyone else have any input?



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