5.3 The Fundamental Theorem of Calculus/27

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