integral subtitusi dari ∫ x (x+4)5 dx = ....

jawab

∫ x (x + 4)⁵ dx

substitusi
u  = x+ 4 → x = u - 4
du = dx

∫ x (x + 4)⁵ dx = ∫ (u-4)(u)⁵ du
= ∫ u⁶ - 4u⁵ du
= 1/7 u⁷ - 4/6 u⁶ + c
= 1/7 (x+4)⁷ - 2/3 (x+4)⁶ + c
= 1/21 (x+4)⁶ { 3(x+4) - 14} + c
= 1/21 (x+4)⁶  (3x +12 - 14) + c
= 1/21 (3x -2 )(x+4)⁶ + c