hasil integral parsial dari 2x(3x-4) dx

pakai substitusi bisa
misal 3x - 4 = u
3x = u + 4
x = (u + 4)/3
u = 3x - 4
du = 3dx
dx = du/3

2x(3x - 4) dx
ubah x ke u
= 2(u+4)/3 (u) du/3
= {2/(3×3)} (u + 4)u du
= (2/9) (u² + 4u) du
integralkan
= (2/9) {⅓u³ + 2u²} + C
= (2/9) (⅓){u³ + 6u²} + C
= (2/27) {u³ + 6u²} + C
= (2/27) u²(u + 6) + C
kembalikan u ke bentuk x
= (2/27) (3x - 4)²(3x - 4 + 6) + C
= (2/27)(3x - 4)²(3x + 2) + C