Answer
\[ - \frac{7}{z} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\frac{7}{{{z^2}}}dz} \hfill \\
Write\,\,\frac{1}{{{z^2}}}\,as\,\,{z^{ - 2}} \hfill \\
\int_{}^{} {7{z^{\,\, - 2}}dz} \hfill \\
Use\,\,the\,\,power\,\,rule \hfill \\
\int_{}^{} {{z^n}dz} = \frac{{{z^{n + 1}}}}{{n + 1}} + C \hfill \\
Then \hfill \\
\int_{}^{} {7{z^{ - 2}}dz} = 7\,\left( {\frac{{{z^{ - 2 + 1}}}}{{ - 2 + 1}}} \right) + C \hfill \\
Simplifying \hfill \\
7\,\left( {\frac{{{z^{ - 1}}}}{{ - 1}}} \right) + C \hfill \\
- \frac{7}{z} + C \hfill \\
\end{gathered} \]
