Answer
\[ = - \frac{1}{3}{p^2}{e^{ - 3p}} - \frac{2}{9}p{e^{ - 3p}} - \frac{4}{{27}}{e^{ - 3p}} + C\]
Work Step by Step
\[\begin{gathered}
\int_{}^{} {{p^2}{e^{ - 3p}}dp} \hfill \\
\hfill \\
Integrate\,\,using\,\,the\,\,formula\, \hfill \\
\hfill \\
\int_{}^{} {{x^n}{e^{ax}}dx} = \frac{1}{a}{x^n}{e^{ax}} - \frac{n}{a}\int_{}^{} {{x^{n - 1}}{e^{ax}}dx} \hfill \\
\hfill \\
therefore \hfill \\
\hfill \\
\int_{}^{} {{p^2}{e^{ - 3p}}dp} = - \frac{1}{3}{p^2}{e^{ - 3p}} - \frac{2}{{ - 3}}\int_{}^{} {x{e^{ - 3p}}dp} \hfill \\
\hfill \\
= - \frac{1}{3}{p^2}{e^{ - 3p}} + \frac{2}{3}\,\,\left[ {\frac{1}{{ - 3}}p{e^{ - 3p}} - \frac{1}{3}\int_{}^{} {{e^{ - 3p}}dp} } \right] \hfill \\
\hfill \\
simplify \hfill \\
\hfill \\
= - \frac{1}{3}{p^2}{e^{ - 3p}} - \frac{2}{9}p{e^{ - 3p}} - \frac{4}{{27}}{e^{ - 3p}} + C \hfill \\
\end{gathered} \]
