Answer
$$12{m^5} - \frac{{50}}{3}{m^3} + C$$
Work Step by Step
$$\eqalign{
& \int {5m\left( {12{m^3} - 10n} \right)} dm \cr
& {\text{multiply}} \cr
& \int {\left( {60{m^4} - 50{m^2}} \right)} dm \cr
& {\text{use power rule for indefinite integrals}} \cr
& = \frac{{60{m^{4 + 1}}}}{{4 + 1}} - \frac{{50{m^{2 + 1}}}}{{2 + 1}} + C \cr
& = \frac{{60{m^5}}}{5} - \frac{{50{m^3}}}{3} + C \cr
& {\text{simplify}} \cr
& = 12{m^5} - \frac{{50}}{3}{m^3} + C \cr
& \cr
& \cr
& {\text{check the antiderivative by differentiation}} \cr
& {\text{ = }}\frac{d}{{ds}}\left( {12{m^5} - \frac{{50}}{3}{m^3} + C} \right) \cr
& = 12\left( 5 \right){m^4} - \frac{{50}}{3}\left( 3 \right){m^2} + 0 \cr
& = 60{m^4} - 50{m^2} \cr
& {\text{factor}} \cr
& = 5m\left( {12{m^3} - 10m} \right) \cr} $$
