  We present analytical results for master integrals emerging in the
computation of differential rates for inclusive weak decays of heavy flavors at
next-to-leading order (NLO) in QCD. As an immediate physical application, these
master integrals allow for a calculation of the spectra of the leptonic
invariant mass in inclusive semileptonic decays in the framework of the heavy
quark expansion, including the NLO QCD corrections to power suppressed terms.
