Integral 2x(6-x) pangkat 5 dx

Integral Substitusi.

∫ 2x(6 - x)⁵ dx = 2 ∫ x(6 - x)⁵ dx
u = 6 - x → x = 6 - u
du / dx = -1 → dx = -du
= -2 ∫ (6 - u)u⁵ du
= -2 ∫ (6u⁵ - u⁶) du
= -2 (u⁶ - 1/7 u⁷) + C
= 2/7 (6 - x)⁷ - 2(6 - x)⁶ + C
= (6 - x)⁶ [2 - 2/7 (6 - x)] + C
= (6 - x)⁶ (2/7 + 2/7 x) + C
= 2/7 (6 - x)⁶ (x + 1) + C