Answer
\[6{t^{ - 1.5}} - 2\ln \left| t \right| + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {\,\left( { - 9{t^{ - 2.5}} - 2{t^{ - 1}}} \right)dt} \hfill \\
Use\,\,the\,\,sum\,\,and\,\,difference\,\,rules \hfill \\
\int_{}^{} { - 9{t^{ - 2.5}}dt} - \int_{}^{} {\,\left( { - 2{t^{ - 1}}} \right)} dt \hfill \\
- 9\int_{}^{} {{t^{ - 2.5}}dt} - 2\int_{}^{} {\frac{1}{t}dt} \hfill \\
Integrate\,\,use\,\,the\,\,power\,\,rule\,\,\,and \hfill \\
\int_{}^{} {\frac{1}{x}dx} = \ln \left| x \right| + C \hfill \\
Then \hfill \\
- 9\,\left( {\frac{{{t^{ - 2.5 + 1}}}}{{ - 2.5 + 1}}} \right) - 2\,\left( {\ln \left| t \right|} \right) + C \hfill \\
Simplifying \hfill \\
- 9\,\left( {\frac{{{t^{ - 1.5}}}}{{ - 1.5}}} \right) - 2\ln \left| t \right| + C \hfill \\
6{t^{ - 1.5}} - 2\ln \left| t \right| + C \hfill \\
\end{gathered} \]
