∫ 0 1 x 4 5 d x = x 4 5 + 1 4 5 + 1 | 0 1 = x 9 5 9 5 | 0 1 = 5 ⋅ 1 9 5 9 − 5 0 9 5 9 = 5 9 {\displaystyle {\begin{aligned}\int _{0}^{1}x^{\frac {4}{5}}dx&={\frac {x^{{\frac {4}{5}}+1}}{{\frac {4}{5}}+1}}{\bigg |}_{0}^{1}={\frac {x^{\frac {9}{5}}}{\frac {9}{5}}}{\bigg |}_{0}^{1}\\[2ex]&={\frac {5\cdot {\sqrt[{5}]{1^{9}}}}{9}}-{\frac {5{\sqrt[{5}]{0^{9}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}}
![{\displaystyle {\begin{aligned}\int _{0}^{1}x^{\frac {4}{5}}dx&={\frac {x^{{\frac {4}{5}}+1}}{{\frac {4}{5}}+1}}{\bigg |}_{0}^{1}={\frac {x^{\frac {9}{5}}}{\frac {9}{5}}}{\bigg |}_{0}^{1}\\[2ex]&={\frac {5\cdot {\sqrt[{5}]{1^{9}}}}{9}}-{\frac {5{\sqrt[{5}]{0^{9}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/ec6f2ec86be59e5ca27122d3b2ff414fb7514044)