Question

$\underset{-2}{\overset{3}{\int }}\frac{1}{x+7}dx$

Answer 1

$$\begin{gathered} \mathrm{Let}I={\int }_{-2}^3\frac{1}{x+7}\mathit{d}x.\mathrm{Then}, \\ I={\left[\log \left(x+7\right)\right]}_{-2}^3 \\ \Rightarrow I=\log 10-\log 5 \\ \Rightarrow I=\log \frac{10}{5}\left[\because \log a-\log b=\log \frac{a}{b}\right] \\ \Rightarrow I=\log 2 \end{gathered}$$