Selesaikan integral berikut dengan cara subtitusi ∫ x (3x -4)⁴ dx

#F

∫ x (3x -4)⁴ dx

u = 3x – 4 → 3x = u + 4 → x = 1/3 (u + 4)

du = 3 dx → dx = 1/3 du

∫ x (3x -4)⁴ dx = ∫ 1/3 (u + 4) (u)⁴ (1/3)du

= ∫ 1/9 (u+4)(u)⁴ du = 1/9 ∫ u⁵ + 4u⁴ du

= 1/9 ( ¹/₆ u⁶ + ⁴/₅ u⁵) + c

= (¹/₉)(¹/₃₀ )(u⁵)(u + 1) + c

= ¹/₂₇₀ (3x -4)⁵ (3x – 4 + 1) + c

= ¹/₂₇₀ (3x – 4)⁵ (3x – 3) + c

= (¹/₂₇₀)(3)(x – 1)(3x – 4)⁵+ c

= ³/₂₇₀ (x – 1)(3x – 4)⁵ + c

= ¹/₉₀ (x – 1)(3x – 4)⁵ + c