Recent detections of the starburst galaxies M82 and NGC 253 by gamma-ray telescopes suggest that galaxies rapidly forming massive stars are more luminous at gamma-ray energies compared to their quiescent relatives. Building upon those results, we examine a sample of 69 dwarf, spiral, and luminous and ultraluminous infrared galaxies at photon energies 0.1-100 GeV using 3 years of data collected by the Large Area Telescope (LAT) on the textit{Fermi Gamma-ray Space Telescope} (textit{Fermi}). Measured fluxes from significantly detected sources and flux upper limits for the remaining galaxies are used to explore the physics of cosmic rays in galaxies. We find further evidence for quasi-linear scaling relations between gamma-ray luminosity and both radio continuum luminosity and total infrared luminosity which apply both to quiescent galaxies of the Local Group and low-redshift starburst galaxies (conservative $P$-values $lesssim0.05$ accounting for statistical and systematic uncertainties). The normalizations of these scaling relations correspond to luminosity ratios of $log(L_{0.1-100 rm{GeV}}/L_{1.4 rm{GHz}}) = 1.7 pm 0.1_{rm (statistical)} pm 0.2_{rm (dispersion)}$ and $log(L_{0.1-100 rm{GeV}}/L_{8-1000 murm{m}}) = -4.3 pm 0.1_{rm (statistical)} pm 0.2_{rm (dispersion)}$ for a galaxy with a star formation rate of 1 $M_{odot}$ yr$^{-1}$, assuming a Chabrier initial mass function. Using the relationship between infrared luminosity and gamma-ray luminosity, the collective intensity of unresolved star-forming galaxies at redshifts $0<z<2.5$ above 0.1 GeV is estimated to be 0.4-2.4 $times 10^{-6}$ ph cm$^{-2}$ s$^{-1}$ sr$^{-1}$ (4-23% of the intensity of the isotropic diffuse component measured with the LAT). We anticipate that $sim10$ galaxies could be detected by their cosmic-ray induced gamma-ray emission during a 10-year textit{Fermi} mission.
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