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

Using termwise division gives LaTeX:  \displaystyle f(x) = 3 x - 7 - \frac{4}{x} + \frac{3}{x^{2}} . Finding the antiderivative of each term gives LaTeX:  \displaystyle F(x) = \frac{3 x^{2}}{2} - 7 x - 4 \ln{\left(x \right)} - \frac{3}{x} + C