The value of $\smallint \,\,\frac{{{x^2} + 1}}{{{x^4} - {x^2} + 1}}\,\,dx$ is

${\tan ^{ - 1}}\,\,\left( {2{x^2} - \,\,1} \right)\,\, + \,\,c$

${\tan ^{ - 1}}\,\,\frac{{{x^2} + \,\,1}}{x}\,\, + \,\,c$

${\sin ^{ - 1}}\,\,\left( {x\,\, - \,\,\frac{1}{x}} \right)\,\, + \,\,c$

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JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

The value of

\int \,\,\frac{{{x^2} + 1}}{{{x^4} - {x^2} + 1}}\,\,dx

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Correct option: D

{\tan ^{ - 1}}\,\,\left( {\frac{{{x^2}\,\, - \,\,1}}{x}} \right)\,\, + \,\,c

Option D is correct because the integral of (x² + 1)/(x⁴ - x² + 1) is solved by dividing by x² and using a substitution, resulting in arctan((x² - 1)/x) + c.

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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