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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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∫  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 the integral is solved by dividing by x2x^2 and then using a substitution.

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