Antiderivative question?

Find the antiderivative by using substitution. Be sure to state clearly what you choose š‘¢ to
be. Show each of the steps and use š¶ as your constant of integration.

(integral) (2x)/(3x^2 - 4)^3

Brainard2016-11-07T06:22:20Z

āˆ«((2x)/(3x^2 - 4)^3)dx

Let u = 3x^2 - 4

Then du = 6xdx

dx = du/6x

āˆ«((2x)/(3x^2 - 4)^3)dx

= āˆ«( 2x/u^3 * du/6x

= 1/3āˆ« u^-3 du

= 1/3 [ - 1/2 u^-2] + C

= - 1/[6(3x^2 - 4)^2] + C

cidyah2016-11-07T06:18:24Z

āˆ« 2x / (3x^2-4)^3 dx

Let u=3x^2-4
du = 6x dx
x dx = (1/6) du

āˆ« 2x / (3x^2-4)^3 dx = (2)(1/6) āˆ« du/ u^3
= (1/3) āˆ« 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

Randy P2016-11-07T06:13:22Z

u = 3x^2 - 4 seems a logical choice since the numerator becomes part of du.