Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 334: 24

$3\ln(1+x^{\frac{1}{3}})+C$

let u = $1+x^{\frac{1}{3}}$ du = $\frac{1}{3}x^{-\frac{2}{3}}dx= \frac{1}{3x^{\frac{2}{3}}}$ $\int\frac{1}{x^{\frac{2}{3}}(1+x^{\frac{1}{3}})}dx$ $=3\int\frac{1}{u}du$ $=3ln(u)+C$ $=3\ln(1+x^{\frac{1}{3}})+C$