∫ x 3 − 2 x x d x = ∫ ( x 3 x − 2 x x ) d x = ∫ ( x 2 − 2 x 1 2 − 1 ) d x = ∫ ( x 2 − 2 x − 1 2 ) d x = x 3 3 − 2 x 1 2 1 2 + C = x 3 3 − 4 x + C {\displaystyle {\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}}}
![{\displaystyle {\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/d9036c97e28b6a10bf32c94f735a344417552a31)