# How to calculate the integral $\int_0^\infty {\rm d}k\, k^{d-1} \frac{1}{\exp(\beta(E_k+\mu))+1}$?

How to calculate the integral $\int_0^\infty {\rm d}k\, k^{d-1} \frac{1}{\exp(\beta(E_k+\mu))+1}$? Here $E_k=\sqrt{a*k^2-b^2}$, and you can think $a, b, d, \mu$ is Real constant.

I don't now how to calculate it, and I use Wolfram Mathematica also can't get any useful information.

• What's $\beta$ ? – Nosrati Jul 30 '18 at 11:09
• Also a real constant. – J.W Kang Jul 30 '18 at 13:15