  In this paper, we analytically investigate the properties of holographic
superconductors in higher dimensions in the framework of Born-Infeld
electrodynamics taking into account the backreaction of the spacetime using the
Sturm-Liouville eigenvalue method. In the background of pure Einstein and
Gauss-Bonnet gravity, based on a perturbative approach, we obtain the relation
between the critical temperature and the charge density. Higher value of the
backreaction and Born-Infeld parameters result in a harder condensation to form
in both cases. The analytical results are found to agree with the existing
numerical results. We also derive an expression for the condensation operator
in $d$-dimensions which yields the critical exponent to be $1/2$.
