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Antiderivative question?
Find the antiderivative by using substitution. Be sure to state clearly what you choose 𝑢 to
be. Show each of the steps and use 𝐶 as your constant of integration.
(integral) (2x)/(3x^2 - 4)^3
3 Answers
- BrainardLv 74 years ago
∫((2x)/(3x^2 - 4)^3)dx
Let u = 3x^2 - 4
Then du = 6xdx
dx = du/6x
∫((2x)/(3x^2 - 4)^3)dx
= ∫( 2x/u^3 * du/6x
= 1/3∫ u^-3 du
= 1/3 [ - 1/2 u^-2] + C
= - 1/[6(3x^2 - 4)^2] + C
- cidyahLv 74 years ago
∫ 2x / (3x^2-4)^3 dx
Let u=3x^2-4
du = 6x dx
x dx = (1/6) du
∫ 2x / (3x^2-4)^3 dx = (2)(1/6) ∫ du/ u^3
= (1/3) ∫ u^(-3) du
= (1/3) u^(-3 +1)/(-3 +1)
= (1/3)(-1/2) u^(-2)
= -1 /(6u^2)
replace u by (3x^2-4)
= -1 /(6(3x^2-4)^2) + C
