5.4 Indefinite Integrals and the Net Change Theorem/11

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