Answer
\[ = \ln \left| {x + \sqrt {{x^2} + 16} } \right| + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + 16} }}} \hfill \\
\hfill \\
use\,\,the\,\,formula\,\,\int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + {a^2}} }}} \hfill \\
with\,a = 4 \hfill \\
\hfill \\
then \hfill \\
\hfill \\
integrate \hfill \\
\hfill \\
\int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + 16} }}} = \ln \left| {x + \sqrt {{x^2} + {a^2}} } \right| + C \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
= \ln \left| {x + \sqrt {{x^2} + 16} } \right| + C \hfill \\
\hfill \\
\end{gathered} \]
