Answer
$$ - \frac{2}{{9{x^3}}} + C$$
Work Step by Step
$$\eqalign{
& \int {\frac{2}{{3{x^4}}}} dx \cr
& {\text{drop out the constant}} \cr
& = \frac{2}{3}\int {\frac{1}{{{x^4}}}} dx \cr
& {\text{power property of exponents }}\frac{1}{{{x^n}}} = {x^{ - n}} \cr
& = \frac{2}{3}\int {{x^{ - 4}}} dx \cr
& {\text{use }}\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C} \cr
& = \frac{2}{3}\left( {\frac{{{x^{ - 3}}}}{{ - 3}}} \right) + C \cr
& {\text{simplifying}} \cr
& = - \frac{2}{9}{x^{ - 3}} + C \cr
& = - \frac{2}{{9{x^3}}} + C \cr} $$
