hasil integral x^2 akar 2x-1dx adalah

misal
u = 2x - 1 => 2x = u + 1 => x = (u + 1)/2
du/dx = 2 => dx = du/2

int (x^2 √(2x - 1)) dx
= int ((u + 1)/2)^2 √u du/2
= int (u^2 + 2u + 1)/4 . u^1/2 . 1/2 du
= int (u^5/2 + 2u^3/2 + u^1/2) / 8 du
= int (1/8 u^5/2 + 1/4 u^3/2 + 1/8 u^1/2) du
= (1/8)/(7/2) u^(7/2) + (1/4)/(5/2) u^(5/2) + (1/8)/(3/2) u^(3/2) + C
= (1/28) u^(7/2) + (1/10) u^(5/2) + (1/12) u^(3/2) + C
= 1/28 u^3 √u + 1/10 u^2 √u + 1/12 u√u + C
= 1/28 (2x - 1)^3 √(2x - 1) + 1/10 (2x - 1)^2 √(2x - 1) + 1/12 (2x - 1) √(2x - 1) + C