Answer
$ 7x^{0.6}+\displaystyle \frac{x^{1.4}}{4.2}-2e^{x}+C$
Work Step by Step
Written in exponent form,
applying Sum and Difference Rules,
... $=\displaystyle \int 4.2x^{-0.4}dx+\int\frac{1}{3}x^{0.4}dx-\int 2e^{x}dx$
... Constant Multiple Rule
$=4.2\displaystyle \int x^{-0.4}dx+\frac{1}{3}\int x^{0.4}dx-2\int e^{x}dx$
... first two: Power Rule, $n\neq-1$
.... third: $\displaystyle \int e^{x}dx=e^{x}+C$,
$=4.2\displaystyle \cdot\frac{x^{0.6}}{0.6}+\frac{1}{3}\cdot\frac{x^{1.4}}{1.4}-2e^{x}+C$
$=7x^{0.6}+\displaystyle \frac{x^{1.4}}{4.2}-2e^{x}+C$
