Numerous scientific fields including astrophysics, nuclear power, and nuclear forensics require a knowledge of basic nuclear properties for large numbers of short-lived, radioactive isotopes far removed from stable nuclei. Neutron-capture cross sections are one such piece of nuclear data where direct measurements are not possible and theoretical predictions can vary by orders of magnitude. A recently developed indirect technique for inferring neutron capture rates, the β-Oslo method, has been introduced but not compared against a known, directly measured neutron capture cross section. To provide this benchmark, two indirect methods based on β decay and charged-particle reactions were used to extract the nuclear level density and γ-ray strength function of Ti51. The nuclear level density and γ-ray strength function from the two data sets were found to be equivalent and were used to extract the neutron capture cross section of Ti50 which agrees with previous direct measurements at high neutron energies. The results demonstrate the validity of the β-Oslo method for extracting neutron capture cross sections of short-lived nuclei and provide a sufficiently small uncertainty to be used in various applications.