Answer
\[ - \frac{1}{{3x}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{1}{{3{x^2}}}} dx \hfill \\
Write\,\,\frac{1}{{{x^2}}}\,\,\,as\,\,{x^{ - 2}} \hfill \\
\int_{}^{} {\frac{1}{{3{x^2}}}dx} = \int_{}^{} {\frac{1}{3}{x^{ - 2}}dx} \hfill \\
\frac{1}{3}\int_{}^{} {{x^{ - 2}}dx} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\
\frac{1}{3}\,\left( {\frac{{{x^{ - 2 + 1}}}}{{ - 2 + 1}}} \right) + C \hfill \\
Simplifying \hfill \\
\frac{1}{3}\,\left( {\frac{{{x^{ - 1}}}}{{ - 1}}} \right) + C \hfill \\
- \frac{1}{{3x}} + C \hfill \\
\end{gathered} \]
