Integrate x / (2 + 3x)^2 plz? Why did partial fractions give me the right answer but doing it by parts didnt

Ok so integrating by parts I got
[-x / 3(2 + 3x)] + [(1/9) ln (2 + 3x)] + C
and when I used partial fractions i got
[(1/9) ln (2 + 3x)] + [2/ 9(2 + 3x)] + C
which is the right answer, but why didnt it work doing it by parts? or did i make some mistake?

[2/ 9(2 + 3x)] - [-x / 3(2 + 3x)] = constant
Therefore, both answers are correct.
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For your additional question:
Because the solution contains a constant, so as long as the difference between two solutions is a constant, the two solutions are essentially the same.

both correct

between [-x / 3(2 + 3x)] and [2/ 9(2 + 3x)] differs by a constant