Answer
$ \displaystyle \frac{x^{3}}{3}+\cdot\frac{3x^{-5}}{10}+C$
Work Step by Step
Expand (multiply out) the integrand,
...$=\displaystyle \int(x^{-2+4}-\frac{3}{2}x^{-2-4})dx=\int(x^{2}-\frac{3}{2}x^{-6})dx$
... Sum and Difference RuIes,
$=\displaystyle \int x^{2}dx-\int\frac{3}{2}x^{-6}dx$
... Constant MultipIe Rule
$=\displaystyle \int x^{2}dx-\frac{3}{2}\int x^{-6}dx$
... both integrals: Power Rule, $n\neq-1$
$=\displaystyle \frac{x^{3}}{3}-\frac{3}{2}\cdot\frac{x^{-5}}{-5}+C$
$=\displaystyle \frac{x^{3}}{3}+\cdot\frac{3x^{-5}}{10}+C$
