  This work deals with modified gravity in five dimensional spacetime. We study
a thick Palatini $f(R)$ brane, that is, a braneworld scenario described by an
anti-de Sitter warped geometry with a single extra dimension of infinite
extent, sourced by real scalar field under the Palatini approach, where the
metric and the connection are regarded as independent degrees of freedom. We
consider a first-order framework which we use to provide exact solutions for
the scalar field and warp factor. We also investigate a perturbative scenario
such that the Palatini approach is implemented through a Lagrangian
$f(R)=R+\epsilon R^n$, where the small parameter $\epsilon$ controls the
deviation from the standard thick brane case.
