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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1
∫  x2−1x4+x2+1  dx\int \,\,\frac{{{x^2} - 1}}{{{x^4} + {x^2} + 1}}\,\,dx is equal to
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Correct option: C
12  log⁡  x2  −  x  +  1x2  +  x  +  1  +  c\frac{1}{2}\,\,\log \,\,\frac{{{x^2}\,\, - \,\,x\,\, + \,\,1}}{{{x^2}\,\, + \,\,x\,\, + \,\,1}}\,\, + \,\,c
Option C (12  log⁡  x2 − x + 1x2 + x + 1 + c\frac{1}{2}\,\,\log \,\,\frac{{{x^2}\, - \,x\, + \,1}}{{{x^2}\, + \,x\, + \,1}}\, + \,c) is correct because after dividing by x2x^2 and using substitution, the integral can be solved to obtain this result.

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