# Math Help - intergrate

1. ## intergrate

intergral of 3x/3x-2 dx

2. Originally Posted by homerb
intergral of 3x/3x-2 dx
Note that $\displaystyle \frac{3x}{3x - 2} = \frac{(3x - 2) + 2}{3x - 2} = 1 + \frac{2}{3x - 2}$.

3. $\frac{3x}{3x-2}=1+\frac{2}{3x-2}$

now it's easy to integrate

4. So, after that do i do u= 3x-2
du= 3 dx? or what is the next step?

5. Originally Posted by homerb
So, after that do i do u= 3x-2
du= 3 dx? [snip]
Yes.

6. my answer comes to x+(2/3)ln[3x-2]+c, is that correct?

7. $x+\frac{2}{3}ln|3x-2|+c$

NOTE: differentiate and you can check your answer for yourself