Given F=$(ye^{z} + 2xy, xe^z + x^2, xye^z)$, we want to evaluate the line $\int_c F*dr$. To get the equation, we integrate $f_x$, $f_y$, and $f_z$. Our professor gave us that the equation should be $f(x,y,z) = xye^z + x^2y$, but I'm getting $f(x,y,z) = 2xye^z + x^2y$. This is because I find both $f_x$ and $f_y$ to be $y(x^2+xe^z)$, which when added with $f_z$'s $xye^z$ we see $yx^z+xye^z+xye^z$.
tl;dr: Wouldn't $xye^z+xye^z = 2xye^z$?