Chapter 8 - Further Techniques and Applications of Integration - 8.1 Integration by Parts - 8.1 Exercises - Page 432: 2

$$\int (x+6) e^{x} d x =(x+5)e^x+c$$

Since $$\int(x+6) e^{x} d x$$ Let \begin{align*} u&= x+6\ \ \ \ \ dv=e^xdx\\ du&= dx\ \ \ \ \ \ \ \ \ \ \ v=e^x \end{align*} Then integrate by parts , we get \begin{align*} \int (x+6) e^{x} d x&=(x+6)e^x-\int e^xdx\\ &=(x+6)e^x- e^x+c\\ &=xe^x+5e^x+c \end{align*}