integral 2x(3x-5)^6 dx=?

Integral Substitusi.

∫ 2x(3x - 5)⁶ dx = 2 ∫ x(3x - 5)⁶ dx
u = 3x - 5 → x = (u + 5) / 3
du / dx = 3 → dx = du / 3
= 2 ∫ u⁶ [(u + 5) / 3] [du / 3]
= 2/9 ∫ (u⁷ + 5u⁶) du
= 2/9 (1/8 u⁸ + 5/7 u⁷) + C
= 1/36 (3x - 5)⁸ + 10/63 (3x - 5)⁷ + C
= (3x - 5)⁷ [10/63 + 1/36 (3x - 5)] + C
= 1/252 [(3x - 5)⁷ (21x + 5)] + C