hasil integral 4x(x-2)^3 dx = hal 14

Integral Substitusi.
Kelompok wajib kelas XI SMA kurikulum 2013 revisi 2016.

∫ 4x(x - 2)³ dx
u = x - 2 → x = u + 2
du / dx = 1
= 4 ∫ (u + 2)u³ du
= 4 ∫ (u⁴ + 2u³) du
= 4 (1/5 u⁵ + 1/2 u⁴) + C
= 4/5 (x - 2)⁵ + 2(x - 2)⁴ + C
= (x - 2)⁴ [2 + 4/5 (x - 2)] + C
= (x - 2)⁴ (4/5 x + 2/5) + C
= 2/5 (x - 2)⁴ (2x + 1) + C

4x(x-2)^3 dx = 4x^4 - 24x^3 + 48x^2 - 32x dx
= (4/5)x^5 - (24/4)x^4 + (48/3)x^3 - (32/2)x^2 + C
= (4/5)x^5 - 6x^4 + 16x^3 - 16x^2 + C