First solve for $P$ in terms of $V$ and $T$ :
$\begin{align*}P = \frac{RT}{V - b} - \frac{a}{V^2}\end{align*}$
The differential work done by the gas is $dW = P dV$ , so the total work done by the gas is
$\begin{align*}\int_1^2 P dV &= \int_{V_1}^{V_2} \left(\frac{RT}{V - b} - \frac{a}{V^2} \right) dV \\&= RT\int_{V_1}^{...$
Therefore, answer (D) is correct.

Solution to 2008 Problem 79