Answer
$$ - \frac{1}{x} - \frac{4}{{3{x^{3/2}}}} + C$$
Work Step by Step
$$\eqalign{
& \int {\left( {\frac{1}{{{x^2}}} - \frac{2}{{{x^{5/2}}}}} \right)} dx \cr
& {\text{write with negative exponents}} \cr
& = \int {\left( {{x^{ - 2}} - 2{x^{ - 5/2}}} \right)} dx \cr
& {\text{sum rule}} \cr
& = \int {{x^{ - 2}}} dx - \int {2{x^{ - 5/2}}} dx \cr
& {\text{integrate by the power rule}} \cr
& = \frac{{{x^{ - 1}}}}{{ - 1}} - \frac{{2{x^{ - 3/2}}}}{{3/2}} + C \cr
& {\text{simplify}} \cr
& = - \frac{1}{x} - \frac{4}{{3{x^{3/2}}}} + C \cr} $$
