Answer
$\frac{3}{7}(x-5)^{7/3}+\frac{15}{2}(x-5)^{4/3}+C$
Work Step by Step
Let u=x-5
then du=dx and x=u+5
thus $\int (x+5)(x-5)^{1/3}dx$
=$\int (u+10)u^{1/3}dx$
=$\int (u^{1/3}+10u^{1/3})du$
=$\frac{3}{7}u^{7/3}+\frac{15}{2}u^{4/3}+C$
=$\frac{3}{7}(x-5)^{7/3}+\frac{15}{2}(x-5)^{4/3}+C$
