Answer
$$ = -{{24\sqrt{6}\,\ln \left(3\,x^2+2\right)-135\,\sqrt{6}\, \ln \left(x+3\right)-58\,\sqrt{6}\,\ln \left(x+1\right)+61\, \arctan \left({{3\,x}\over{\sqrt{6}}}\right)}\over{145\,\sqrt{6}}} $$
Explanation
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