$\begin{align}  & \int\limits_{1}^{4}{\sqrt{(x+5)}dx}=\int\limits_{1}^{4}{{{(x+5)}^{\tfrac{1}{2}}}dx}=\left[ \frac{2}{3}{{(x+5)}^{\tfrac{3}{2}}} \right]_{1}^{4} \\ & \text{      } \\ & \int\limits_{1}^{4}{\sqrt{(x+5)}dx}=\frac{2}{3}\left[ {{(4+5)}^{\tfrac{3}{2}}}-{{(1+5)}^{\tfrac{3}{2}}} \right] \\ & \int\limits_{1}^{4}{\sqrt{(x+5)}dx}=\frac{2}{3}\left[ 27-14.7 \right]=8.2 \\\end{align}$