Show that the vector field is conservative if
\textbf{F}(x, y, z) = \left< \frac{e^z}{(1 + x^2)^2}, \sin^2 y, \frac{1}{2} \left( \frac{x}{x^2 + 1} + \tan^{-1} x \right) e^z \right>
and find the line integral $\int_C \textbf{F} \cdot d\textbf{r}$ if $C$ is a curve from $(0, 0, 0)$ to $(1, \pi/2, 1)$.