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

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

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

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

is equal to

View answer and explanation

Correct option: A

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

Option A,

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

, is correct because it is the result of integrating the given function using substitution and partial fractions.