Answer
\begin{aligned}
\int( x^{2}-5x) e^{x} d x = e^{x}(x^2-7x+7)+C
\end{aligned}
Work Step by Step
Given $$\int( x^{2}-5x) e^{x}d x $$
So, we have
\begin{array}{|c c c c|}\hline & Differentiation && {Integration} \\
\hline
+ \quad \rightarrow&x^{2}-5x & & e^{x} \\
&&\searrow&\\ \hline
- \quad \rightarrow& 2x-5 & &e^{x} \\
&&\searrow&\\ \hline
+ \quad \rightarrow&2& &e^{x} \\
&&\searrow&\\ \hline
&0 & &e^{x} \\
&&\\ \hline
\end{array}
Therefore
\begin{aligned}
I&=\int( x^{2}-5x) e^{x} d x\\
&=(x^2-5x)e^{x}-(2x-5)e^{x}+2e^{x}\\
&= e^{x}(x^2-7x+7)+C
\end{aligned}
