5.3 The Fundamental Theorem of Calculus/27

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