Homework Help: Integral from solid state

1. Mar 28, 2012

cscott

1. The problem statement, all variables and given/known data

Trying to solve this integral

$$\int_0^T \frac{dT'}{T'}\frac{d}{dT'}U(T',V)$$

where the temperature dependent part of U is

$$\Sigma \frac{h\omega}{\exp(\beta\omega)-1}$$

3. The attempt at a solution

using x = hw/T I find that I need to integrate

$$\frac{x^3 \exp(x/k)}{(\exp(x/k)-1)^2 h\omega k}$$

with limits going to 0 -> inf and T -> hw/T

I just don't see how with these limits it will work out nicely (the result is used to get the pressure in the harmonic approximation) but I can't find my mistake.