Question

Evaluate: ${\int }_{-2}^3\frac{1}{x+5}dx$.

Answer 1

Let $I={\int }_{-2}^3\frac{1}{x+5}dx$

$={\begin{array}{c}{\log }_e(x+5)\end{array}|}_{-2}^3$

$={\log }_{e}8-{\log }_{e}3$

$={\begin{array}{c}{\log }_{e}8\end{array}|}_3$ or ${\begin{array}{c}ln8\end{array}|}_3$.