Answer
\[{\text{False}}\]
Work Step by Step
\[\begin{gathered}
\int {\ln {e^x}dx} \hfill \\
{\text{False, }}{e^x}{\text{ is the argument of the natural logaritm ln, besides}} \hfill \\
{\text{to solve we first must be simplify }}\ln {e^x}{\text{ to obatin }}x,{\text{ then}} \hfill \\
\int {\ln {e^x}dx} = \int x dx = \frac{{{x^2}}}{2} + C \hfill \\
\end{gathered} \]
