The value of $\mathop \smallint \nolimits_1^2 \,\,\frac{{dx}}{{x\left( {1 + {x^4}} \right)}}$ is

$\frac{1}{4}\,\,\log \,\,\frac{{17}}{{32}}$

$\frac{1}{4}\,\,\log \,\,\frac{{17}}{2}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

The value of

\int \nolimits_1^2 \,\,\frac{{dx}}{{x\left( {1 + {x^4}} \right)}}

View answer and explanation

Correct option: B

\frac{1}{4}\,\,\log \,\,\frac{{32}}{{17}}

Option B (

\frac{1}{4}\,\log \,\frac{{32}}{{17}}

) is correct because after substituting

x^4 = t

and using partial fractions, we can evaluate the definite integral.