Find the work done by the vector field

F$=3+2$xy$2,2$x$2$y$\backslash$vec$\{$F$\}=\backslash$langle $3+2$xy$^2,\backslash 2$x$^2$y $\backslash$rangleF$=3+2$xy$2,2$x$2$y$$

to move a particle along the arc of the hyperbola y$=1$xy $=\backslash$frac$\{1\}\{$x$\}$y$=$x$1$ from $(1,1)(1,1)(1,1)$ to $(4,14)(4,\backslash$frac$\{1\}\{4\})(4,41).$