Answer
$\displaystyle \frac{1}{2}x^{8}+\frac{1}{2}x^{-2}+x+C$
Work Step by Step
Applying: Sum and Difference RuIes
$...=\displaystyle \int 4x^{7}dx-\int x^{-3}dx+\int 1dx$
...Constant MultipIe Rule
$=4\displaystyle \int x^{7}dx-\int x^{-3}dx+\int 1dx$
... Power Rule, $( n\neq-1)$
... last integral: $1=x^{0}$
$=4\displaystyle \cdot\frac{x^{7+1}}{7+1}-\frac{x^{-3+1}}{-3+1}+\frac{x^{0+1}}{0+1}+C$
$=\displaystyle \frac{1}{2}x^{8}+\frac{1}{2}x^{-2}+x+C$
