∫ 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]&=\left[{\frac {5{\sqrt[{5}]{(1)^{9}}}}{9}}\right]-\left[{\frac {5{\sqrt[{5}]{(0)^{9}}}}{9}}\right]\\[2ex]&={\frac {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]&=\left[{\frac {5{\sqrt[{5}]{(1)^{9}}}}{9}}\right]-\left[{\frac {5{\sqrt[{5}]{(0)^{9}}}}{9}}\right]\\[2ex]&={\frac {5}{9}}\end{aligned}}}](https://en.wikipedia.org/api/rest_v1/media/math/render/svg/a8fe31528d21b3d8d15367237fdbee8bc9a97541)