Answer
$$\frac{5}{7}{r^{7/5}} + C$$
Work Step by Step
$$\eqalign{
& \int {\root 5 \of {{r^2}} } dr \cr
& {\text{then}} \cr
& = \int {{r^{2/5}}} dr \cr
& {\text{use power rule for indefinite integrals}} \cr
& = \frac{{{r^{7/5}}}}{{7/5}} + C \cr
& {\text{simplify}} \cr
& = \frac{5}{7}{r^{7/5}} + C \cr
& {\text{check by differentiation}} \cr
& {\text{ = }}\frac{d}{{dr}}\left( {\frac{5}{7}{r^{7/5}} + C} \right) \cr
& = \frac{5}{7}\left( {\frac{7}{5}} \right){r^{2/5}} + 0 \cr
& = {r^{2/5}} \cr
& = \root 5 \of {{r^2}} \cr} $$
