The diffusion of tin $($A$)$ in liquid lead $($B$)$ at $510C$ was carried out by using a $10\mathrm{.}0-mm-$long capillary tube and maintaining the mole fraction of tin at $x_{A1}$ at the left end and $x_{A2}$ at the right end of the tube. In the range of concentration of $0\mathrm{.}2x_{A}0\mathrm{.}4$ the diffusivity of tin in lead has been found to be a linear function of $x_A$:$D_{AB}=A+B{x}_A.($ A and $B$ are constants$).$ Assume the molar density to be constant at $c=c_A+c_B=c_{ar}.$ Drive the final integrated equation for the flux $N_{{?}_{}}$ assuming steady state and that A diffuses through stagnant $B.$

Hint: ${\displaystyle \underset{x}{\overset{n}{}}}\frac{xdx}{a+bx}=\frac{1}{b^2}[a+bx-$aln$(a+bx){]}_{a1}^{x_1}$