Question

Evaluate : $\underset{2}{\overset{3}{\int }}{3}^{x}dx.$

Answer 1

$$\begin{gathered} I={\int }_2^3{3}^x \\ ={\overline{)\frac{3^x}{\log 3}}}_2^3+C(\mathrm{Use}:\int a^x=\frac{a^x}{\log a}+C) \\ =\frac{3^3}{\log 3}-\frac{3^2}{\log 3}+C \end{gathered}$$

$$\begin{gathered} =\frac{1}{\log 3}(3^3-3^2)+C \\ =\frac{1}{\log 3}(27-9)+C \\ =\frac{1}{\log 3}\left(18\right)+C \end{gathered}$$