Find the anti-derivative of $LaTeX: \displaystyle f(x) = 2 x^{3} - 4 x^{2} + 7 x + 4$ .

Using the power rule on each term gives $LaTeX: \displaystyle F(x) = \frac{x^{4}}{2} - \frac{4 x^{3}}{3} + \frac{7 x^{2}}{2} + 4 x + C$