24. $\int x^{4} d x$.
Solution. Apply formula $\mathrm{I}$ for $n=4$ :

$$
\int x^{4} d x=\frac{x^{4+1}}{4+1}+C=\frac{1}{5} x^{5}+C
$$

Verification: $d\left(\frac{1}{5} x^{5}+C\right)=\frac{1}{5} \cdot 5 x^{4} d x=x^{4} d x$. We obtained the integrand; therefore, the integral is found correctly.