Answer
Please see the work below.
Work Step by Step
We know that the force is:
$F=-Kx-cx^3$
and the energy is:
$W=-\int Fdx$
$\implies W=-\int (-kx-cx^3)dx$
$W=k(\frac{x^2}{2})+c(\frac{x^4}{4})$
We plug in the known values to obtain:
$W=(220)(\frac{(0.15)^2}{2})+(3.1)(\frac{(0.15)^4}{4})=2.5J$
