Although it is not defined on all of space $\mathbb{R}^3$, the field associated with the line integral below is defined on a region that is simply connected, and the component test can be used to show it is conservative. Find a potential function for the field and evaluate the integral.
$\int_{(4,1,4)}^{(4,5,8)} 18x^2 dx + \frac{5z^2}{y} dy + 10z \ln y dz$
A general expression for the infinitely many potential functions is $f(x,y,z) = \Box$.
Evaluate the line integral.
$\int_{(4,1,4)}^{(4,5,8)} 18x^2 dx + \frac{5z^2}{y} dy + 10z \ln y dz = \Box$ (Type an exact answer.)