The value of $\mathop \smallint \nolimits_1^{{e^2}} \,\,\frac{{dx}}{{x\,{{(1\,\, + \,\,\log \,\,x)}^2}}}$ is

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \nolimits_1^{{e^2}} \,\,\frac{{dx}}{{x\,{{(1\,\, + \,\,\log \,\,x)}^2}}}

View answer and explanation

Correct option: A

\frac{2}{3}

Option A (

\frac{2}{3}

) is correct because the definite integral evaluates to 2/3 after a simple substitution.

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