The value of $\smallint \,\frac{{{{\left( {x\,\, + \,\,1} \right)}^2}}}{{x\left( {{x^2} + \,\,1} \right)}}\,dx$ is equal to

${\log _e}\,\,\left( {\frac{1}{{{x^2} + \,\,1}}} \right) + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Analyzing +4 | -1

The value of

\int \,\frac{{{{\left( {x\,\, + \,\,1} \right)}^2}}}{{x\left( {{x^2} + \,\,1} \right)}}\,dx

is equal to

View answer and explanation

Correct option: B

{\log _e}\,\,x + 2\,\,{\tan ^{ - 1}}\,\,x\,\, + \,\,c

Option B (

{\log _e}\,x + 2\,{\tan ^{ - 1}}\,x\, + \,c

) is correct because the integrand can be split into simpler fractions, which integrate to this result.