Aims. We present a new measurement of the cosmic X-ray background (CXRB) in the 1.5−7 keV energy band, performed by exploiting the Swift X-ray telescope (XRT) data archive. We also present a CXRB spectral model in a wider energy band (1.5−200 keV), obtained by combining these data with the recently published Swift-BAT measurement. Methods. From the XRT archive we collect a complete sample of 126 high Galactic latitude gamma-ray burst (GRB) follow-up observations. This provides a total exposure

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... f 7.5 Ms and a sky-coverage of ∼7 square degrees which represents a serendipitous survey, well suited for a direct measurement of the CXRB in the 1.5−10 keV interval. Our work is based on a complete characterization of the instrumental background and an accurate measurement of the stray-light contamination and vignetting calibration. Results. We find that the CXRB spectrum in the 1.5−7 keV energy band can be equally well fitted by a single power-law with photon index Γ = 1.47±0.07 or a single power-law with photon index Γ = 1.41±0.06 and an exponential roll-off at 41 keV. The measured flux in the 2−10 keV energy band is 2.18 ± 0.13 × 10 −11 erg cm −2 s −1 deg −2 in the 2−10 keV band. Combining Swift-XRT with Swift-BAT (15−200 keV) we find that, in the 1.5−200 keV band, the CXRB spectrum can be well described by two smoothly-joined power laws with the energy break at 29.0 ± 0.5 keV corresponding to a νF ν peak located at 22.4 ± 0.4 keV. Conclusions. Taking advantage of both the Swift high energy instruments (XRT and BAT), we produce an analytical description of the CXRB spectrum over a wide (1.5−200 keV) energy band. This model is marginally consistent with the HEAO1 measurement (∼10% higher) at energies higher than 20 keV, while it is significantly (30%) higher at low energies (2−10 keV).