Answer
$$\frac{2}{{{x^2}}} + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{{ - 4}}{{{x^3}}}} dx \cr
& {\text{use the property of exponents }}\frac{1}{{{x^n}}} = {x^{ - n}} \cr
& = \int {\left( { - 4{x^{ - 3}}} \right)} dx \cr
& {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr
& = - 4\int {{x^{ - 3}}} dx \cr
& {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = - 4\left( {\frac{{{x^{ - 3 + 1}}}}{{ - 3 + 1}}} \right) + C \cr
& {\text{simplifying}} \cr
& = - 4\left( {\frac{{{x^{ - 2}}}}{{ - 2}}} \right) + C \cr
& = 2{x^{ - 2}} + C \cr
& = \frac{2}{{{x^2}}} + C \cr} $$
