Example 2. Find the integral $\int \frac{x^{4}-2 x^{3}+3 x^{2}}{x^{2}} d x$.
Solution. Dividing term by term the numerator by the denominator, using properties 3 and 4 and formula (4.5), we find

$$
\begin{gathered}
\int \frac{x^{4}-2 x^{3}+3 x^{2}}{x^{2}} d x=\int\left(x^{2}-2 x+3\right) d x=\int x^{2} d x-2 \int x d x+3 \int d x= \\
=\frac{x^{2+1}}{2+1}-2 \frac{x^{1+1}}{1+1}+3 x+C=\frac{x^{3}}{3}-x^{2}+3 x+C
\end{gathered}
$$