The branching ratio of the structure dependent (SD) radiative K+→e+νeγ decay relative to that of the K+→e+νe(γ) decay including the internal bremsstrahlung (IB) process (Ke2(γ)) has been measured in the J-PARC E36 experiment using plastic scintillator/lead sandwich detectors, in contrast to the previous E36 measurement, which used a CsI(Tl) calorimeter. In the analysis, the effect of IB was also taken into account in the SD radiative decay as Ke2γ(γ)SD. By combining the new data with the previous E36 result after revision for the IB correction for Ke2γ(γ)SD, a new value Br(Ke2γ(γ)SD)/Br(Ke2(γ))=1.20±0.07 has been determined. This is consistent with a recent lattice QCD calculation, but larger than the expectation of Chiral Perturbation Theory (ChPT) at order O(p4) and the previous KLOE value. Using the method to relate form factor and branching ratio described in the KLOE paper, the present result is also consistent with the form factor prediction based on a gauged nonlocal chiral quark model, but larger than that from ChPT at order O(p6).