Integrate: 1/(x-sqrt(x+2) dx

I came up with:

(2/3)(2*ln((sqrt(x+2))-2)+ln((sqrt(x+2))-1))

but it keeps coming back the wrong answer even though I integrated correctly. Is there a way to simplify this answer, and if so, how?

I found:

Ln[x-sqrt(x+2)] +

1/3Ln[(sqrt(x+2)-2)/(sqrt(x+2) + 1)]

ok but is there a way to further simplify this answer?

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