5.3 The Fundamental Theorem of Calculus/27

${\begin{aligned}\int _{0}^{2}x(2+x^{5})\,dx&=\int _{0}^{2}(2x+x^{6})\,dx=\int _{0}^{2}(2x+x^{6})\,dx\\[2ex]&=\left({\frac {2x^{1+1}}{1+1}}+{\frac {x^{6+1}}{6+1}}\right){\bigg |}_{0}^{2}=\left(x^{2}+{\frac {x^{7}}{7}}\right){\bigg |}_{0}^{2}\\[2ex]&=\left((2)^{2}-{\frac {(2)^{7}}{7}}\right)-\left((0)^{2}+{\frac {(0)^{7}}{7}}\right)\\[2ex]&=\left[4+{\frac {2^{7}}{7}}\right]-[0]\\[2ex]&={\frac {156}{7}}\end{aligned}}$