$\mathop \smallint \nolimits_0^\infty \,\,\frac{{x\,\,\log \,\,x\;\,\,dx}}{{{{\left( {1 + {x^2}} \right)}^2}}}$ is equal to

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

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\int \nolimits_0^\infty \,\,\frac{{x\,\,\log \,\,x\;\,\,dx}}{{{{\left( {1 + {x^2}} \right)}^2}}}

is equal to

View answer and explanation

Correct option: A

\mathrm{0}

Option A (0) is correct because the integral evaluates to zero due to the symmetry of the integrand after a suitable substitution.

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