$\smallint \frac{{dx}}{{x\left( {{x^5} + 1} \right)}}$ is equal to

$\frac{1}{5}\,\,\log \,\,{x^5}\left( {{x^5} + \,\,1} \right) + c$

$\frac{1}{5}\,\,\log \,\,\left( {\frac{{{x^5} + \,\,1}}{{{x^5}}}} \right) + c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Analyzing +4 | -1

\int \frac{{dx}}{{x\left( {{x^5} + 1} \right)}}

is equal to

View answer and explanation

Correct option: C

\frac{1}{5}\,\,\log \,\,\left( {\frac{{{x^5}}}{{{x^5} + \,\,1}}} \right)\, + c

Option C is correct because the integral can be solved using substitution and partial fractions.