Example 6. Find the integral $\int\left(a x^{3}+b x^{2}+c x+p\right) d x$.
Solution.

$$
\begin{gathered}
\int\left(a x^{3}+b x^{2}+c x+p\right) d x=a \int x^{3} d x+b \int x^{2} d x+c \int x d x+ \\
+p \int d x=\frac{a}{4} x^{4}+\frac{b}{3} x^{3}+\frac{c}{2} x^{2}+p x+C
\end{gathered}
$$