DiogenesTorch
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Homework Statement
This is the integral
<br /> \int \frac{x^2}{e^x-1}dx<br />
Homework Equations
Can this even be solved in closed form?
The Attempt at a Solution
Only method I can think of is integration by parts over numerous steps. I did that until I get the following:
<br /> \int \frac{x^2}{e^x-1}dx = x^2 \ln{(e^x-1)} -\frac{5x^3}{3}-2 \int x \ln{(e^x-1)} dx <br />
Now I am stuck on the last integral above: \int x \ln{(e^x-1)} dx and can't find how to integrate it.
Any ideas or suggestions much appreciated :)