5.3 The Fundamental Theorem of Calculus/27

<math> \begin{align}

\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{align}