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Answer
$$ = {{5\,\sqrt{3}\,\ln \left(x^2+x+1\right)+32\,\sqrt{3}\,\ln \left(2 \,x+3\right)+22\,\arctan \left({{2\,x+1}\over{\sqrt{3}}}\right)-14\, 3\sqrt{3}\,\ln \left(x+1\right)}\over{28\,\sqrt{3}}} $$
Explanation
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