Verify that F = f F = f and evaluate the line integral of F

Verify that $F=\nabla f$ and evaluate the line integral of $F$ over the given path.

\(\mathbf{F}(x, y, z)=\frac{z}{x} \mathbf{i}+\mathbf{j}+\ln x \mathbf{k}, \quad f(x, y, z)=y+z \ln x ;\)

circle \((x-4)^{2}+y^{2}=1\) in the clockwise direction