5.3 The Fundamental Theorem of Calculus/23

${\begin{aligned}\int _{0}^{1}x^{\frac {4}{5}}dx&={\frac {x^{{\frac {4}{5}}+1}}{{\frac {4}{5}}+1}}{\Bigg |}_{0}^{1}={\frac {x^{\frac {9}{5}}}{\frac {9}{5}}}{\Bigg |}_{0}^{1}\\[2ex]&=\left[{\frac {5{\sqrt[{5}]{(1)^{9}}}}{9}}\right]-\left[{\frac {5{\sqrt[{5}]{(0)^{9}}}}{9}}\right]\\[2ex]&={\frac {5}{9}}\end{aligned}}$