Question

Use U-Substitution

∫ 4/[(1+2x)^3]dx

Answer 1

u= 1+2x
du=2dx
dx=du/2

Substitute back to equation,
∫ 4/u^3 (du/2)
∫ 2/u^3 du

- 1/u^2 + c
Substitute u=1+2x into equation,
- 1/(1+2x)^2 + c

Answer 2

∫ 4/[(1+2x)^3]dx
= 4 ∫ dx /[(1+2x)^3]
Let u = 1 + 2x -> du/2 = dx
= 4/2 ∫ du/ u^3 = 2 ( -1/ 2u^2 )
= - 1/u^2 = -1/( 1 +x)^2 + C

Answer 3

I mean
-1/( 1 + 2x)^2 + C