Chapter 8 - Further Techniques and Applications of Integration - 8.1 Integration by Parts - 8.1 Exercises - Page 432: 1

$$\int x e^{x} d x =xe^x- e^x+c$$

Since $$\int x e^{x} d x$$ Let \begin{align*} u&= x\ \ \ \ dv=e^xdx\\ du&= dx\ \ \ \ v=e^x \end{align*} Then integrate by parts , we get \begin{align*} \int x e^{x} d x&=xe^x-\int e^xdx\\ &=xe^x- e^x+c \end{align*}