Answer
$$ - \frac{5}{{3{x^3}}} + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{5}{{{x^4}}}} dx \cr
& {\text{use the property of exponents }}\frac{1}{{{x^n}}} = {x^{ - n}} \cr
& = \int {5{x^{ - 4}}} dx \cr
& {\text{use multiple constant rule }}\int {k \cdot f\left( x \right)} dx = k\int {f\left( x \right)} dx \cr
& = 5\int {{x^{ - 4}}} dx \cr
& {\text{use power rule }}\int {{x^x}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \cr
& = 5\left( {\frac{{{x^{ - 4 + 1}}}}{{ - 4 + 1}}} \right) + C \cr
& {\text{simplifying}} \cr
& = 5\left( {\frac{{{x^{ - 3}}}}{{ - 3}}} \right) + C \cr
& = - \frac{5}{3}{x^{ - 3}} + C \cr
& = - \frac{5}{{3{x^3}}} + C \cr} $$
