5.3 The Fundamental Theorem of Calculus/23

${\begin{aligned}&\int _{0}^{1}x^{\cfrac {4}{5}}dx\\[2ex]&{\cfrac {5\cdot {\sqrt[{5}]{x^{4}}}}{9}}\\[2ex]&{\cfrac {5\cdot {\sqrt[{5}]{x^{4}}}}{9}}{\bigg |}_{0}^{1}\\[2ex]&{\cfrac {5\cdot {\sqrt[{1^{5}}]{1^{4}}}}{9}}-{\cfrac {5\cdot 0{\sqrt[{5}]{0^{4}}}}{9}}\\[2ex]&={\cfrac {5}{9}}\end{aligned}}$