5.4 Indefinite Integrals and the Net Change Theorem/30

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_{1}^{2}\frac{y+5y^7}{y^3}dy &= \int_{1}^{2}\left(\frac{y}{y^3}+\frac{5y^7}{y^3}\right)dy = \int_{1}^{2}(y^{-2}+5y^{4})dy\\[2ex] &= \left(\frac{y^{-2+1}}{-2+1}+\frac{5y^{4+1}}{4+1}\right)\bigg|_{1}^{2} = \left(\frac{y^{-1}}{-1}+y^5\right)\bigg|_{1}^{2} = \left(-\frac{1}{y}+y^5\right)\bigg|_{1}^{2} \\[2ex] &= \left(-\frac{1}{(2)}+(2)^5\right) - \left(-\frac{1}{(1)}+(1)^5\right) \\[2ex] &= \left(-\frac{1}{2}+32\right) = \left(-\frac{1}{2}+\frac{64}{2}\right) = \frac{63}{2} \end{align} }