I performed a u-substitution and got this integral: $$\int_0^\infty \frac{2u}{\sqrt{e^u-1}}du$$ I thought about using IBP but that didn't work. I also thought there was a way to use beta function, but that exponential function is out of the way. How would you go about this?
WolframAlpha says that it numerically equals 8.71034 which is close to $\pi\ln(16)$, but I don't know if this is the exact form for that integral.
