Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 336: 6

$$A=\frac{4\sqrt[4]{x^9}}{9}+C$$

$$A=\int{\sqrt[4] {x^5}}dx$$ $$A=\int{x^{5/4}}dx$$ According to Table 1, we know that $\int{x^n}dx=\frac{x^{n+1}}{n+1}$. Therefore, $$A=\frac{x^{9/4}}{\frac{9}{4}}+C=\frac{4x^{9/4}}{9}+C$$ $$A=\frac{4\sqrt[4]{x^9}}{9}+C$$