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

$\frac{{ - 1}}{{1 + x}}\,\, + \,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The integral

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

is equal to

View answer and explanation

Correct option: B

\frac{{ - 1}}{{1\,\, + \,\,\log \,\,x}}\,\, + \,\,c

Option B (

\frac{{ - 1}}{{1\,\, + \,\,\log \,\,x}}\,\, + \,\,c

) is correct because it is obtained by using a simple u-substitution with

u = 1 + \log x

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