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Improved measurements of the absolute branching fractions of the inclusive decays <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:mi>ϕ</mml:mi><mml:mi>X</mml:mi></mml:mrow></mml:math>
By analyzing 2.93 fb−1 of e+e− annihilation data taken at the center-of-mass energy s=3.773 GeV with the BESIII detector, we determine the branching fractions of the inclusive decays D+→ϕX and D0→ϕX to be (1.135±0.034±0.031)% and (1.091±0.027±0.035)%, respectively, where X denotes any possible particle combination. The first uncertainties are statistical, and …