29. $\int x^{2 / 3} d x$.

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29. $\int x^{2 / 3} d x$.
Solution. $\int x^{2 / 3} d x=\frac{x^{2 / 3+1}}{2 / 3+1}+C=\frac{x^{5 / 3}}{5 / 3}+C=\frac{3}{5} x^{5 / 3}+C=\frac{3}{5} x \sqrt[3]{x^{2}}+$ $+C$.

Verification: $d\left(\frac{3}{5} x \sqrt[3]{x^{2}}+C\right)=d\left(\frac{3}{5} x^{5 / 3}+C\right)=\frac{3}{5} \cdot \frac{5}{3} x^{5 / 3-1} d x=$ $=x^{2 / 3} d x$, i.e., the integral is found correctly.