Chapter 8 - Techniques of Integration - 8.1 Integration by Parts - Exercises - Page 396: 60

$$\int x^n e^x dx = x^n e^x -n\int x^{n-1} e^xdx $$

Given $$\int x^n e^x dx$$ Let \begin{align*} u&=x^n \ \ \ \ \ \ \ \ dv= e^xdx\\ du&= nx^{n-1}\ \ \ \ \ v=e^x \end{align*} Then \begin{align*} \int x^n e^x dx&= x^n e^x -n\int x^{n-1} e^xdx \end{align*}