= Solution
The <Bose-Einstein distribution> gives $n_i=[\exp((E_i-\mu)/(k_BT))-1]^{-1}$, with <chemical potential> below the lowest <energy> when its discrete occupation is finite. In the continuum approximation,
$$
\boxed{N=\int_0^\infty\frac{g(E)}{e^{(E-\mu)/(k_BT)}-1}\,dE,\qquad U=\int_0^\infty\frac{Eg(E)}{e^{(E-\mu)/(k_BT)}-1}\,dE.}
$$
If the zero-energy <ground state> is macroscopically occupied, its discrete occupation $N_0$ must be added to the first integral; it contributes no <energy> to the second. This distinction is essential when applying the formulas to <Bose-Einstein condensation>.
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