Answer
$ 2e^{x}+\displaystyle \frac{5x|x|}{2}+\frac{x}{4}+C$
Work Step by Step
applying Sum and Difference Rules,
... $=\displaystyle \int 2e^{x}dx+\int 5|x|dx+\int\frac{1}{4}dx$
... Constant Multiple Rule
$=2\displaystyle \int e^{x}dx+5\int|x|dx+\frac{1}{4}\int dx$
... first integral: $\displaystyle \int e^{x}dx=e^{x}+C$,
... second: $\displaystyle \int|x|dx=\frac{x|x|}{2}+C$,
$... $third: $\displaystyle \int 1dx=x+C$,
$=2e^{x}+\displaystyle \frac{5x|x|}{2}+\frac{x}{4}+C$
