integral x3(2x-3)2 dx

int x³ (2x -3)² dx
int x³ (4x² - 12x + 9) dx
int  4x⁵ - 12x⁴ + 9x³ dx
= 4/6 x⁶ -12/5 x⁵ + 9/4 x⁴ + c
= 2/3 x⁶ - 12/5 x⁵ + 3/2 x⁴ + c
= 1/30 x⁴ ( 20x² - 72x + 45 ) + c