  We study inflation in the Brans-Dicke gravity as a special model of the
scalar-tensor gravity. We obtain the inflationary observables containing the
scalar spectral index, the tensor-to-scalar ratio, the running of the scalar
spectral index and the equilateral non-Gaussianity parameter in terms of the
general form of the potential in the Jordan frame. Then, we compare the results
for various inflationary potentials in light of the Planck 2015 data. Our study
shows that in the Brans-Dicke gravity, the power-law, inverse power-law and
exponential potentials are ruled out by the Planck 2015 data. But, the hilltop,
Higgs, Coleman-Weinberg and natural potentials can be compatible with Planck
2015 TT,TE,EE+lowP data at 95\% CL. Moreover, the D-brane, SB SUSY and
displaced quadratic potentials can be in well agreement with the observational
data since their results can lie inside the 68\% CL region of Planck 2015
TT,TE,EE+lowP data.
