Chapter 4 - Integrals - 4.4 Indefinite Integrals and the Net Change Theorem - 4.4 Exercises - Page 337: 37

$1$

$\displaystyle \int_0^1\sqrt[4] {x^5}+\sqrt[5] {x^4}dx=\int_0^1x^{5/4}+x^{4/5}dx$ $\displaystyle (\frac{x^{9/4}}{9/4}+\frac{x^{9/5}}{9/5})|_0^1$ $\displaystyle (\frac{4x^{9/4}}{9}+\frac{5x^{9/5}}{9})|_0^1$ $\displaystyle [\frac{4(1)^{9/4}}{9}+\frac{5(1)^{9/5}}{9}]-[\frac{4(0)^{9/4}}{9}+\frac{5(0)^{9/5}}{9}]$ $\displaystyle \frac{4}{9}+\frac{5}{9}-0=\frac{9}{9}$ $1$