5.4 Indefinite Integrals and the Net Change Theorem/6

${\begin{aligned}\int \left({\sqrt {x^{3}}}+{\sqrt[{3}]{x^{2}}}\right)dx&=\int \left(x^{\frac {1}{3}}+x^{\frac {2}{3}}\right)dx\\[2ex]&=\left({\frac {x^{{\frac {1}{3}}+1}}{{\frac {1}{3}}+1}}\right)+\left({\frac {x^{{\frac {2}{3}}+1}}{{\frac {2}{3}}+1}}\right)+C\\[2ex]&={\frac {3x^{\frac {4}{3}}}{4}}+{\frac {3x^{\frac {5}{3}}}{5}}+C\end{aligned}}$