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Measurements of the branching fractions of the inclusive decays <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>D</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>D</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi…
Using ${e}^{+}{e}^{\ensuremath{-}}$ annihilation data corresponding to an integrated luminosity of $2.93\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ taken at a center-of-mass energy of 3.773 GeV with the BESIII detector, we report the first measurements of the branching fractions of the inclusive decays ${D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}X$ and ${D}^{+}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}X$, where pions from ${K}_{S}^{0}$ decays have been excluded from …