Answer
\[ = \frac{1}{3}\arcsin \,\left( {3x} \right) + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{{dx}}{{\sqrt {1 - 9{x^2}} }}} \hfill \\
\hfill \\
rewrite \hfill \\
\hfill \\
= \frac{1}{3}\int_{}^{} {\frac{{3dx}}{{\sqrt {1 - \,{{\left( {3x} \right)}^2}} }}} \hfill \\
\hfill \\
integrate\,\, \hfill \\
\hfill \\
= \frac{1}{3}\arcsin \,\left( {3x} \right) + C \hfill \\
\end{gathered} \]
