5.3 The Fundamental Theorem of Calculus/23

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