(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate ∫ 3x /(3x+1)^2.dx , with limits 1 & 0

using the sustitution u = 3x+1

2. Relevant equations

3. The attempt at a solution

u= 3x+1

du/dx = 3

dx = du/3

Therefore,

∫ 3x*(u)^-2 * du/3

= ∫ x* (u)^-2

Since u = 3x +1

Therefore, x = (u-1)/3

Hence,

∫ (u-1)* 1/3*(u^2)

Now, plugging in limits of 1&0 into u

u = 3(1) +1 =4

u = 3(0) + 1 = 1

Therefore, limits of 4 & 1.

Hence,

1/3 ∫ (u^-1)-(u^-2)

=1/3 [-u + 2u^-1] with limits 4& 1.

= 1/3 (- 9/2) = -3/2.

However, there is no answer mathing this solution.

But i dont know where i went wrong??

please help.

thankyou.

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# Homework Help: Integration, u substitution with limits

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