Answer
$$\frac{9}{2}{x^{4/3}} + C$$
Work Step by Step
$$\eqalign{
& \int {6\root 3 \of x } dx \cr
& = 6\int {\root 3 \of x } dx \cr
& = 6\int {{x^{1/3}}} dx \cr
& {\text{use power rule for indefinite integrals}} \cr
& = 6\left( {\frac{{{x^{4/3}}}}{{4/3}}} \right) + C \cr
& {\text{simplify}} \cr
& = \frac{9}{2}{x^{4/3}} + C \cr
& {\text{check by differentiation}} \cr
& {\text{ = }}\frac{d}{{dx}}\left( {\frac{9}{2}{x^{4/3}} + C} \right) \cr
& = \frac{9}{2}\left( {\frac{4}{3}} \right){x^{1/3}} + C \cr
& = 6{x^{1/3}} + C \cr
& = 6\root 3 \of x + C \cr} $$
