Answer
$ \displaystyle \frac{1,000\cdot 0.9^{x}}{\ln 0.9}-\frac{2x|x|}{5}+C$
Work Step by Step
applying Sum and Difference RuIes,
... $=\displaystyle \int 1,000(0.9^{x})dx+\int\frac{4}{5}|x|dx$
... Constant MultipIe Rule
$=1,000\displaystyle \int 0.9^{x}dx+\frac{4}{5}\int|x|dx$
... 1st integral: $\displaystyle \int b^{x}dx=\frac{b^{x}}{\ln b}+C$
... 2nd integral: $\displaystyle \int|x|dx=\frac{x|x|}{2}+C$
$=1,000\displaystyle \cdot \frac{0.9^{x}}{\ln 0.9}-\frac{4}{5}\cdot\frac{x|x|}{2}+C$
$= \displaystyle \frac{1,000\cdot 0.9^{x}}{\ln 0.9}-\frac{2x|x|}{5}+C$
