Chapter 13 - Section 13.2 - Substitution - Exercises - Page 971: 35

$\int x(x-2)^5dx=\frac{1}{7}(x-2)^7+\frac{1}{3}(x-2)^6+C$

Substitution: $u=x-2$ $x=u+2$ $dx=du$ $\int x(x-2)^5dx=\int (u+2)u^5du=\int (u^6+2u^5)du=\frac{1}{7}u^7+\frac{2}{6}u^6+C=\frac{1}{7}(x-2)^7+\frac{1}{3}(x-2)^6+C$