Answer
$G\left( x \right) = 12{x^{1/3}} - \frac{3}{4}{x^{8/3}} + C$
Work Step by Step
$$\eqalign{
& g\left( x \right) = 4{x^{ - 2/3}} - 2{x^{5/3}} \cr
& {\text{Using the formulas in Table 2 }}\left( {{\text{see page 358}}} \right){\text{ }} \cr
& {\text{Function: }}cf\left( x \right) \to {\text{Particular antiderivative: }}cF\left( x \right) \cr
& {\text{Function: }}{x^n}\left( {n \ne - 1} \right) \to {\text{Particular antiderivative: }}cF\left( x \right) \cr
& {\text{Function: }}f\left( x \right) + h\left( x \right) \to {\text{Particular antiderivative: }}f\left( x \right) + h\left( x \right) \cr
& {\text{And applying the Theorem 1}},{\text{ we obtain}} \cr
& G\left( x \right) = 4\left( {\frac{{{x^{ - 2/3 + 1}}}}{{ - 2/3 + 1}}} \right) - 2\left( {\frac{{{x^{5/3 + 1}}}}{{5/3 + 1}}} \right) + C \cr
& G\left( x \right) = 4\left( {\frac{{{x^{1/3}}}}{{1/3}}} \right) - 2\left( {\frac{{{x^{8/3}}}}{{8/3}}} \right) + C \cr
& G\left( x \right) = 12{x^{1/3}} - \frac{3}{4}{x^{8/3}} + C \cr} $$
