∫ 0 1 x 3 + x 2 3 d x = ∫ 0 1 x 3 2 + x 2 3 d x = ( 2 x 5 2 5 + 3 x 5 3 5 ) | 0 1 = 2 5 + 3 5 = 1 {\displaystyle \int _{0}^{1}{{\sqrt {x^{3}}}+x^{\frac {2}{3}}dx}=\int _{0}^{1}{x^{\frac {3}{2}}+x^{\frac {2}{3}}dx}=\left.\left({\frac {2x^{\frac {5}{2}}}{5}}+{\frac {3x^{\frac {5}{3}}}{5}}\right)\right|_{0}^{1}={\frac {2}{5}}+{\frac {3}{5}}=1}
