∫ ( x 3 + x 2 3 ) d x = ∫ ( x 1 3 + x 2 3 ) d x = ( x 1 3 + 1 1 3 + 1 ) + ( x 2 3 + 1 2 3 + 1 ) + C = 3 x 4 3 4 + 3 x 5 3 5 + C {\displaystyle {\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}}}
![{\displaystyle {\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}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/312a99f3d852c0cea28ac6796131dfed725d38dd)