∫ 25x(5x-3)^(4) dx = ...
A. (1/30)(5x-3)^(5)(25 x+...

Question

∫ 25x(5x-3)^(4) dx = ...
A. (1/30)(5x-3)^(5)(25 x+3)+C
B. (1/30)(5x-3)^(5)(25 x-18)+C
C. (1/30)(5x-3)^(5)(15 x+18)+C
D. (1/30)(5x-3)^(5)(15 x-3)+C
E. (1/30)(5x-3)^(5)(15 x-18)+C

G. Widosamodra · Accepted Answer

Jawaban yang benar adalah A. (1/30)(5x - 3)⁵(25x + 3) + C

Pembahasan :
Konsep :
∫u dv = uv - ∫vdu
∫ ax^n dx = a/(n+1) x^(n+1) + c
y = ax^n maka dy/dx = anx^(n-1)

∫ 25x (5x - 3)⁴ dx

u = 25x
du/dx = 25 
du = 25 dx

dv = (5x - 3)⁴ dx
v = 1/5 . 1/5 . (5x - 3)⁵
v = 1/25.(5x - 3)⁵

∫u dv = uv - ∫vdu
∫25x (5x - 3)⁴ dx = (25x)(1/25.(5x - 3)⁵) - ∫1/25.(5x - 3)⁵ . 25 dx
= x(5x - 3)⁵ - ∫(5x - 3)⁵ dx
= x(5x - 3)⁵ - 1/5 . 1/6 . (5x - 3)⁶ + C
= x(5x - 3)⁵ - 1/30 (5x - 3)⁶ + C
= x(5x - 3)⁵ - 1/30 (5x - 3)(5x - 3)⁵ + C
= 1/30. 30x (5x - 3)⁵ - 1/30 (5x - 3)(5x - 3)⁵ + C
= (1/30)(5x - 3)⁵(30x - (5x - 3)) + C
= (1/30)(5x - 3)⁵(30x - 5x + 3) + C
= (1/30)(5x - 3)⁵(25x + 3) + C

Jadi, ∫25x (5x - 3)⁴ dx = (1/30)(5x - 3)⁵(25x + 3) + C
Opsi yang benar adalah A.
Semoga membantu ya.

∫ 25x(5x-3)^(4) dx = ... A. (1/30)(5x-3)^(5)(25 x+3)+C B. (1/30)(5x-3)^(5)(25 x-18)+C C. (1/30)(5x-3)^(5)(15 x+18)+C D. (1/30)(5x-3)^(5)(15 x-3)+C E. (1/30)(5x-3)^(5)(15 x-18)+C

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