Inelasticity--the fraction of a neutrinos energy transferred to hadrons--is a quantity of interest in the study of astrophysical and atmospheric neutrino interactions at multi-TeV energies with IceCube. In this work, a sample of contained neutrino interactions in IceCube is obtained from 5 years of data and classified as 2650 tracks and 965 cascades. Tracks arise predominantly from charged-current $ u_{mu}$ interactions, and we demonstrate that we can reconstruct their energy and inelasticity. The inelasticity distribution is found to be consistent with the calculation of Cooper-Sarkar et al. across the energy range from $sim$ 1 TeV to $sim$ 100 TeV. Along with cascades from neutrinos of all flavors, we also perform a fit over the energy, zenith angle, and inelasticity distribution to characterize the flux of astrophysical and atmospheric neutrinos. The energy spectrum of diffuse astrophysical neutrinos is well-described by a power-law in both track and cascade samples, and a best-fit index $gamma=2.62pm0.07$ is found in the energy range from 3.5 TeV to 2.6 PeV. Limits are set on the astrophysical flavor composition that are compatible with a ratio of $left(frac{1}{3}:frac{1}{3}:frac{1}{3}right)_{oplus}$. Exploiting the distinct inelasticity distribution of $ u_{mu}$ and $bar{ u}_{mu}$ interactions, the atmospheric $ u_{mu}$ to $bar{ u}_{mu}$ flux ratio in the energy range from 770 GeV to 21 TeV is found to be $0.77^{+0.44}_{-0.25}$ times the calculation by Honda et al. Lastly, the inelasticity distribution is also sensitive to neutrino charged-current charm production. The data are consistent with a leading-order calculation, with zero charm production excluded at $91%$ confidence level. Future analyses of inelasticity distributions may probe new physics that affects neutrino interactions both in and beyond the Standard Model.
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