$\smallint \,\,\frac{{dx}}{{x\left( {{x^7} + 1} \right)}}$ is equal to

$\log \,\,\left( {\frac{{{x^7} + 1}}{{{x^7}}}} \right) + c$

$\frac{1}{7}\,\,\log \,\,\left( {\frac{{{x^7} + 1}}{{{x^7}}}} \right) + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,\frac{{dx}}{{x\left( {{x^7} + 1} \right)}}

is equal to

View answer and explanation

Correct option: B

\frac{1}{7}\,\,\log \,\,\left( {\frac{{{x^7}}}{{{x^7} + 1}}} \right) + c

Option B (

\frac{1}{7}\,\log \,\left( {\frac{{{x^7}}}{{{x^7} + 1}}} \right) + c

) is correct because after substitution and partial fraction decomposition, the integral evaluates to this expression.