Answer
$ \displaystyle \frac{100\cdot 1.1^{x}}{\ln 1.1}-\frac{x|x|}{3}+C$
Work Step by Step
applying Sum and Difference RuIes,
... $=\displaystyle \int 100(1.1^{x})dx+\int\frac{2}{3}|x|dx$
... Constant Multiple Rule
... $=100\displaystyle \int 1.1^{x}dx+\frac{2}{3}\int|x|dx$
... 1st integral: $\displaystyle \int b^{x}dx=\frac{b^{x}}{\ln b}+C$
... 2nd integral: $\displaystyle \int|x|dx=\frac{x|x|}{2}+C$
$=100\displaystyle \cdot \frac{1.1^{x}}{\ln 1.1}-\frac{2}{3}\cdot\frac{x|x|}{2}+C$
$= \displaystyle \frac{100\cdot 1.1^{x}}{\ln 1.1}-\frac{x|x|}{3}+C$
