Find the anti-derivative of LaTeX:  \displaystyle f(x) = \frac{2 x^{3} + 6 x^{2} - 7 x - 5}{x}

Using termwise division gives LaTeX:  \displaystyle f(x) = 2 x^{2} + 6 x - 7 - \frac{5}{x} . Finding the antiderivative of each term gives LaTeX:  \displaystyle F(x) = \frac{2 x^{3}}{3} + 3 x^{2} - 7 x - 5 \ln{\left(x \right)} + C