5.3 The Fundamental Theorem of Calculus/27

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \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} }