Find the anti-derivative of LaTeX:  \displaystyle f(x) = \frac{5 x^{3} - 6 x^{2} + 5 x - 5}{x^{2}}

Using termwise division gives LaTeX:  \displaystyle f(x) = 5 x - 6 + \frac{5}{x} - \frac{5}{x^{2}} . Finding the antiderivative of each term gives LaTeX:  \displaystyle F(x) = \frac{5 x^{2}}{2} - 6 x + 5 \ln{\left(x \right)} + \frac{5}{x} + C