  We generalize the analytical investigation on the properties of $s$-wave
holographic superconductors in the presence of Born-Infeld nonlinear
electrodynamics by taking the backreaction into account. We find that in the
presence of nonlinear gauge field, one can still employ the analytical method
when the backreaction is turned on. Our calculation is based on the
Sturm-Liouville eigenvalue problem, which is a variational method. For the
system under consideration, we obtain the relation between the critical
temperature and the charge density. We find that both backreaction and
Born-Infeld parameters decrease the critical temperature of the superconductor
and make the condensation harder. At the ned of paper, we calculate the
critical exponent associated with the condensation near the critical
temperature and find that it has the universal value $1/2$ of the mean field
theory.
