Answer
-$\frac{1}{2}$$(7-\frac{r^{5}}{10})^{4}$
Work Step by Step
u=7- $\frac{r^{5}}{10}$ =$\gt$ du= - $\frac{5r^{4}}{10}$dr =$\gt$ -2du=$r^{4}$dr
substition : $\int$(7-$\frac{r^{5}}{10}$)$^{3}$$r^{4}$dr= $\int$$u^{3}$(-2du)=-2$\int$$u^{3}$du
-2$\int$$4^{3}$=-2($\frac{u^{3+1}}{3+1}$)+C= -$\frac{1}{2}$$u^{4}$+C
So, u=7-$\frac{r^{5}}{10}$ we get -$\frac{1}{2}$$(7-\frac{r^{5}}{10})^{4}$
