Question

Integrate: $\int (x-1)(x-2)dx$

Answer 1

$\int (x-1)(x-2)dx$

$=\int (x^2-x-2x+2)dx$

$=\int (x^2-3x+2)dx$

$=\int x^{2}dx-3\int xdx+2\int dx$

$=\frac{x^3}{3}-3\frac{x^2}{2}+2x+C$

$=\frac{x^3}{3}-\frac{3x^2}{2}+2x+C$

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