Consider $$\int \frac{x^2}{1+e^{-x}}dx$$
I've tried every method and trick that I'm familiar with, except by parts, but I can't seem to be able to acquire an elementary integral. Does there exist one? If so, what would it be?
2026-04-13 04:24:03.1776054243
Evaluating $\int \frac{x^2}{1+e^{-x}}dx$
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According to Mathematica, this integral cannot be expressed as a combination of elementary functions. The provided answer is:
$$ I = x^2 \ln{(1+e^{-x})} + 2x \, \mathrm{Li}_2 (e^{-x}) -2 \, \mathrm{Li}_3(-e^x), $$ where $\mathrm{Li}_n(x)$ is the polylogarithm function.
Hope this helps.
Cheers!
I have just noticed that you find out the answer (at least partially) by yourself. Please let me know if my answer should be removed.