Answer
$$\displaystyle{\int x^ne^x\ dx=x^ne^x-n\int x^{n-1}e^x\ dx}$$
Work Step by Step
$\displaystyle{I=\int x^ne^x\ dx}$
$\displaystyle \left[\begin{array}{ll} u=x^n & dv=e^x \\ & \\ du=nx^{n-1} & v=e^x \end{array}\right]$ Integration by parts
$\displaystyle{I=x^ne^x-\int e^x\times nx^{n-1}\ dx}\\
\displaystyle{I=x^ne^x-n\int x^{n-1}e^x\ dx}$
