We describe a technique that enhances the sensitivity of a spectrometer for trace gas detection employing an external cavity continuously tunable CW quantum cascade laser and integrating the absorption spectra across multiple lines of the species. We demonstrate the power of this method by continuously recording the absorption spectra of $\mathrm{N}{\mathrm{O}}_2$ across the R branch from 1628.8 to $1634.5{\mathrm{cm}}^{-1}$ . By integrating the resulting spectra, the detection sensitivity of $\mathrm{N}{\mathrm{O}}_2$ is improved by a factor of 15 compared to the sensitivity achieved using single line laser absorption spectroscopy with the same apparatus. This procedure offers much shorter data acquisition times for the real-time monitoring of trace gas species compared to adding repeated scans of the spectra to improve the signal-to-noise ratio.