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

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log⁡x4+x2+1+C

log⁡x2−x+1x2+x+1+C

12log⁡x2−x+1x2+x+1+C

12log⁡x2+x+1x2−x+1+C

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detailed solution

Correct option is C

∫x2−1x4+x2+1dx⇒ I=∫1−1x2x2+1x2+1dx=∫1−1x2x+1x2−1dx Put x+1x=t⇒1−1x2dx=dt∴ I=∫dtt2−12=12×1log⁡t−1t+1+C =12log⁡x2+1−xx2+1+x+C

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∫x2−1x4+x2+1dx is equal to

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