Hasil dari integral x(1-2x)pangkat 3 dx adalah......

Integral dgn substitusi
u  = 1 - 2x
du = - 2 dx
dx= -1/2 du ...(1)

u =1 - 2x
-2x  = u - 1
x = - 1/2(u - 1)

∫ x (1- 2x)³ dx =
= ∫ - 1/2 (u-1)(u)³(-1/2 du)
= ∫1/4 (u-1)(u³) du
= 1/4 ∫ (u-1)u³ du
= 1/4 ∫ u⁴ - u³ du
= 1/4 (1/5 u⁵ - 1/4 u⁴) + c
= 1/20 u⁵ - 1/16 u⁴ +C
= 1/80 u⁴ (4 u - 5) + C
= 1/80 (1-2x)⁴ {4(1-2x) - 5} +c
= 1/80 (1-2x)⁴ (4-8x -5)+c
= 1/80 (1-2x)⁴(-1-8x) + c
= - 1/80 (1+8x)(1-2x)⁴ + c