  In this paper, we investigate chaotic inflation from scalar field subjected
to potential in the framework of $f(R^2, P, Q)$-gravity, where we add a
correction to Einstein's gravity based on a function of the square of the Ricci
scalar $R^2$, the contraction of the Ricci tensor $P$, and the contraction of
the Riemann tensor $Q$. The Gauss-Bonnet case is also discussed. We give the
general formalism of inflation, deriving the slow-roll parameters, the
$e$-folds number, and the spectral indexes. Several explicit examples are
furnished, namely we will consider the cases of massive scalar field and scalar
field with quartic potential and some power-law function of the curvature
invariants under investigation in the gravitational action of the theory.
Viable inflation according with observations is analyzed.
