∫ 0 1 x 4 5 d x 5 ⋅ x 4 5 9 | 0 1 5 ⋅ 1 4 9 − 5 0 4 5 9 = 5 9 {\displaystyle {\begin{aligned}&\int _{0}^{1}x^{\cfrac {4}{5}}dx\\[2ex]&{\cfrac {5\cdot {\sqrt[{5}]{x^{4}}}}{9}}{\bigg |}_{0}^{1}\\[2ex]&{\cfrac {5\cdot {\sqrt {1^{4}}}}{9}}-{\cfrac {5{\sqrt[{5}]{0^{4}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}}
![{\displaystyle {\begin{aligned}&\int _{0}^{1}x^{\cfrac {4}{5}}dx\\[2ex]&{\cfrac {5\cdot {\sqrt[{5}]{x^{4}}}}{9}}{\bigg |}_{0}^{1}\\[2ex]&{\cfrac {5\cdot {\sqrt {1^{4}}}}{9}}-{\cfrac {5{\sqrt[{5}]{0^{4}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/df80ba568e9e3ad889253aedf85bef74078cfc19)