Evaluate the integrals \int (2-3x)(3+2x)(1-2x)dx

∫(2 – 3x)(3 + 2x)(1 – 2x) dx

= ∫(6 + 4x – 9x – 6x²)(1 – 2x) dx

= ∫(6 – 5x – 6x²)(1 – 2x) dx

= ∫(6 – 5x – 6x² – 12x + 10x² + 12x³) dx

= ∫(6 – 17x + 4x² + 12x³) dx

Upon splitting the above, we have

= ∫6 dx – ∫17x dx + ∫4x² dx + ∫12x³ dx

On integrating using formula,

∫xⁿ dx =\(\dfrac{ x^{n+1}}{n+1}\)

we get

= 6x – \( \dfrac{17}{(1+1)}\) x¹⁺¹ + \( \dfrac{4}{2+1}\) x²⁺¹ + \( \dfrac{12}{3+1}\) x³⁺¹ + c

= \( 6x – \dfrac{17x^2}{2} +\dfrac{ 4x^3}{3} + 3x^4 + c\)