The integral ∫2x−3×2+x+12 dx is equal to

The integral $\int \frac{2x-3}{{\left({x}^{2}+x+1\right)}^{2}}$ dx is equal to

1. A

$-\frac{1}{{x}^{2}+x+1}-\frac{16}{3\sqrt{3}}{\mathrm{tan}}^{-1}\frac{2x+1}{\sqrt{3}}-\frac{4}{3}\left(\frac{2x+1}{{x}^{2}+x+1}\right)+C$

2. B

$-\frac{1}{{x}^{2}+x+1}-\frac{16}{3\sqrt{3}}{\mathrm{tan}}^{-1}\frac{2x-1}{\sqrt{3}}+\frac{4}{3}\left(\frac{2x-1}{{x}^{2}+x+1}\right)+C$

3. C

$\frac{1}{2\left({x}^{2}+x+1\right)}-\frac{\left(2x+1{\right)}^{2}}{{\left({x}^{2}+x+1\right)}^{2}}+C$

4. D

$\frac{1}{4\left({x}^{2}+x+1\right)}+\frac{2}{3}{\mathrm{tan}}^{-1}\left(2x+1\right)+C$

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