Question

A. Integral (3x-1)^3dx =
B.integral (x-2)(x^2-4x-5)^-4 dx =

Answer 1

Verified answer

Jawab

a.  ∫(3x -1)³ dx
u = 3x - 1
du = 3 dx
dx = 1/3 du

∫(3x -1)³ dx = 1/3  ∫ u³ du = 1/3. 1/4 u⁴ +c
= 1/12 u⁴ + c
= 1/12 (3x -1)⁴ + c

b. ∫ (x -2) (x² -4x -5)⁻⁴ dx

u = x² - 4x - 5
du = 2x - 4 dx
du = 2(x -2) dx
(x- 2) dx = 1/2 du

∫ (x-2) (x² - 4x - 5)⁻⁴ dx =  1/2 ∫  u⁻⁴ du
= 1/2.  (-1/3)  u⁻³ + c
= -1/6 (x² -4x - 5)⁻³ + c