integral(6x-12)(√x^2-4x+8)dx

6 int (x - 2)√(x² - 4x + 8) dx
u = x² - 4x + 4 → du = (2x - 4) dx → du = 2(x - 2) dx
(x - 2) dx = (1/2) du
= 6(1/2) int √u du
= 3 int u^(1/2) du
= 3(2/3)u^(3/2) + c
= 2(x² - 4x + 8)^(3/2) + c, atau
= 2(x² - 4x + 8)√(x² - 4x + 8) + c