Answer
$\displaystyle \frac{3}{5}x^{2}+2x^{-1}-\frac{1}{4}x^{-4}+4x+C$
Work Step by Step
Applying: Sum and Difference RuIes
$...=\displaystyle \int 3x^{4}dx-\int 2x^{-2}dx+\int x^{-5}dx+\int 4dx$
...Constant MultipIe Rule
$=3\displaystyle \int x^{4}dx-2\int x^{-2}dx+\int x^{-5}dx+4\int 1dx$
... Power Rule,$( n\neq-1)$
... last integral: $1=x^{0}$
$=3\displaystyle \cdot\frac{x^{4+1}}{4+1}-2\cdot\frac{x^{-2+1}}{-2+1}+\frac{x^{-5+1}}{-5+1}+4\cdot\frac{x^{0+1}}{0+1}+C$
$=\displaystyle \frac{3}{5}x^{2}+2x^{-1}-\frac{1}{4}x^{-4}+4x+C$
