Answer
$12.2x^{0.5}+\displaystyle \frac{x^{1.5}}{9}-e^{x}+C$
Work Step by Step
Written in exponent form,
applying Sum and Difference Rules,
... $=\displaystyle \int 6.1x^{-0.5}dx+\int\frac{1}{6}x^{0.5}dx-\int e^{x}dx$
... Constant Multiple Rule
... $=6.1\displaystyle \int x^{-0.5}dx+\frac{1}{6}\int x^{0.5}dx-\int e^{x}dx$
... first two: Power Rule, $n\neq-1$
.... third: $\displaystyle \int e^{x}dx=e^{x}+C$,
$=6.1\displaystyle \cdot\frac{x^{0.5}}{0.5}+\frac{1}{6}\cdot\frac{x^{1.5}}{1.5}-e^{x}+C$
$=12.2x^{0.5}+\displaystyle \frac{x^{1.5}}{9}-e^{x}+C$
