The value of $\mathop \smallint \nolimits_{{e^{ - 1}}}^e \,\,\frac{{dt}}{{t\,\,\left( {1 + t} \right)}}$ is equal to

$\log \,\,\left( {\frac{e}{{1 + e}}} \right)$

$\log \,\,\left( {\frac{1}{{1 + e}}} \right)$

JEE MATHEMATICS MCQ: DEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

The value of

\int \nolimits_{{e^{ - 1}}}^e \,\,\frac{{dt}}{{t\,\,\left( {1 + t} \right)}}

is equal to

View answer and explanation

Correct option: D

\mathrm{1}

Option D (1) is correct because the integral can be solved by partial fraction decomposition and evaluating the resulting logarithmic terms.

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