Question

$\int \left(2-3x\right)\left(3+2x\right)\left(1-2x\right)dx$

Answer 1

$$\begin{gathered} \int \left(2-3x\right)\left(3+2x\right)\left(1-2x\right)dx \\ =\int \left(2-3x\right)\left(3-6x+2x-4x^2\right)dx \\ =\int \left(2-3x\right)\left(-4x^2-4x+3\right)dx \\ =\int \left(-8x^2-8x+6+12x^3+12x^2-9x\right)dx \\ =\int \left(12x^3+4x^2-17x+6\right)dx \\ =\frac{12x^4}{4}+\frac{4x^3}{3}-\frac{17x^2}{2}+6x+C \\ =3x^4+\frac{4}{3}{x}^3-\frac{17}{2}{x}^2+6x+C \end{gathered}$$