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We report a measurement of the cross section for the process e+e−→π+π−J/ψ around the X(3872) mass in search for the direct formation of e+e−→X(3872) through the two-photon fusion process. No enhancement of the cross section is observed at the X(3872) peak and an upper limit on the product of electronic width and branching fraction of X(3872)→π+π−J/ψ is determined to be Γee×B(X(3872)→π+π−J/ψ)<7.5×10−3eV at 90% confidence level under an assumption of total width of 1.19±0.21 MeV. This is an improvement of a factor of about 17 compared to the previous limit. Furthermore, using the latest result of B(X(3872)→π+π−J/ψ), an upper limit on the electronic width Γee of X(3872) is obtained to be <0.32eV at the 90% confidence level.