The problem is to determine the Fermi velocity for a fermion gas at absolute zero. the problem using integrating a function that looks like
$$ v = \frac{4\pi V}{h^{3}} m^{3} \int_{0}^{\infty}{ \frac{v_{f}^{3} \, dv}{e^{\frac{\frac{mv_{f}^{2}}{2} - \mu}{kt}} + 1} } $$
which is supposed to equal $ \frac{3 v_{f}}{4}$. It also mentions something about integrating by parts. Does anyone know how to integrate that?
Thank you.