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If $\int \frac{x + 1}{(x^{2} + x + 1)} \frac{d x}{\sqrt{x^{2} + x + 1}} = k \frac{x - 1}{\sqrt{x^{2} + x + 1}} + C$ then the value of $k$

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Correct option is C

Differentiating both the sides w.r.t.x, and simplifying , we get x+1x2+x+13/2=3k2x+1x2+x+13/2⇒k=23

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If ∫x+1x2+x+1dxx2+x+1=kx−1x2+x+1+C then the value of k

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If $\int \frac{x + 1}{(x^{2} + x + 1)} \frac{d x}{\sqrt{x^{2} + x + 1}} = k \frac{x - 1}{\sqrt{x^{2} + x + 1}} + C$ then the value of $k$