Using 2.93~fb$^{-1}$ of data taken at 3.773 GeV with the BESIII detector operated at the BEPCII collider, we study the semileptonic decays $D^+ to bar K^0e^+ u_e$ and $D^+ to pi^0 e^+ u_e$. We measure the absolute decay branching fractions $mathcal B(D^+ to bar K^0e^+ u_e)=(8.60pm0.06pm 0.15)times10^{-2}$ and $mathcal B(D^+ to pi^0e^+ u_e)=(3.63pm0.08pm0.05)times10^{-3}$, where the first uncertainties are statistical and the second systematic. We also measure the differential decay rates and study the form factors of these two decays. With the values of $|V_{cs}|$ and $|V_{cd}|$ from Particle Data Group fits assuming CKM unitarity, we obtain the values of the form factors at $q^2=0$, $f^K_+(0) = 0.725pm0.004pm 0.012$ and $f^{pi}_+(0) = 0.622pm0.012pm 0.003$. Taking input from recent lattice QCD calculations of these form factors, we determine values of the CKM matrix elements $|V_{cs}|=0.944 pm 0.005 pm 0.015 pm 0.024$ and $|V_{cd}|=0.210 pm 0.004 pm 0.001 pm 0.009$, where the third uncertainties are theoretical.
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