Energy & Spring Displacement function

[TheWhiteKnyt]

Homework Statement

What would be the energy required to stretch a spring of $$\vec{F}spring = - (ax+βx^2)\hat{x}$$ where$$\vec{x} = x*\hat{x}$$

Homework Equations

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$$\vec{A}/|A| = \hat{A}$$
$$|\vec{A}| = sqrt(A*A)$$
$$A = (A^x)^2 + (A^y)^2$$

The Attempt at a Solution

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So far I'm at a loss just getting started.

 

[BvU]

Hello White, welcome to PF :)

To get started:
Do you know the energy required to stretch a spring of $\vec F = -a\vec x$ ? How was that expression derived ?