The short story is, that I have to calculate some transport coefficients, but using the the MB distribution as my distribution function. What I currently need to solve is:
${{\mathcal{L}}^{\,\left( \alpha \right)}}=\frac{1}{2}\frac{{\bar{N}}}{V}{{\left( \frac{{{h}^{2}}}{2\pi m{{k}_{B}}T} \right)}^{3/2}}\frac{1}{{{k}_{B}}T}\int{{{e}^{-\varepsilon /{{k}_{B}}T}}}{{\left( \varepsilon -\mu \right)}^{\alpha }}{{\varepsilon }^{3/2}}d\varepsilon$
As it shows, it's not that the integral is hard, it's more what I use for $\mu$ that is my concern. According to my teacher I need to use:
${{e}^{-\mu /{{k}_{B}}T}}=\frac{1}{2}\frac{V}{{\bar{N}}}{{\left( \frac{2\pi m{{k}_{B}}T}{{{h}^{2}}} \right)}^{3/2}}$
But I can't see how I can use this instead of $\mu$ without solving for $\mu$. And then I would just end up with a ln() term, which I really can't imagine doing anything good for me. But maybe I'm mistaken ?
Any hint would be appreciated :)