\(\int \frac{x^{2}-1}{x^{4}+x^{2}+1}dx\) is equal to

\(\frac{1}{2}\log \frac{x^{2}+x-1}{x^{2}+x+1}+c\) \(\frac{1}{2}\log \frac{x^{2}+x+1}{x^{2}-x+1}+c\) \(\frac{1}{2}\log \frac{x^{2}-x+1}{x^{2}+x+1}+c\) None of these

\(\frac{1}{2}\log \frac{x^{2}-x+1}{x^{2}+x+1}+c\)

\(\begin{aligned}\int \frac{x^{2}-1}{x^{4}+x^{2}+1}dx&=\int \frac{1-\frac{1}{x^{2}}}{\left(x+\frac{1}{x}\right)^{2}-1}dx\\ &=\int \frac{dt}{t^{2}-1} \text{ where }x+\frac{1}{x}=t\end{aligned}\)