5.4 Indefinite Integrals and the Net Change Theorem/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_{1}^{4}\sqrt{t}(1+t)dt &=\int_{1}^{4}\left(t^{\frac{1}{2}}+t^{\frac{3}{2}}\right)dt \\[2ex] &=\left(\frac{2t^{\frac{3}{2}}}{3}+\frac{2t^{\frac{5}{2}}}{5}\right)\Bigg|_{1}^{4} \\[2ex] &=\left[\frac{2(4)^{\frac{3}{2}}}{3}+\frac{2(4)^{\frac{5}{2}}}{5}\right]-\left[\frac{2(1)^{\frac{3}{2}}}{3}+\frac{2(1)^{\frac{5}{2}}}{5}\right] \\[2ex] &=\left[\frac{16}{3}+\frac{64}{5}\right]-\left[\frac{2}{3}+\frac{2}{5} \right] \\[2ex] &=\frac{256}{15} \end{align} }