- #1
DiogenesTorch
- 11
- 0
Homework Statement
This is the integral
[tex]
\int \frac{x^2}{e^x-1}dx
[/tex]
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:
[tex]
\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
[/tex]
Now I am stuck on the last integral above: [itex]\int x \ln{(e^x-1)} dx[/itex] and can't find how to integrate it.
Any ideas or suggestions much appreciated :)